
m 






— . 



*mA ^H 1 1 




t^ .cOiiw.,. * 




ROBERT BEALL, 
8nxcn AND STiTIO.VKB, 

rcnns 7 lT»iii»ATBmj., 




THE GREAT TELESCOPE OF THE UNITED STATES NAVAL OBSERVA- 
TORY, WASHINGTON. 

CONSTRUCTED BY ALVAN CLARK AND SONS, 1873. 



POPUIAR ASTRONOMY. 




BY 



SIMON NEWCOMB, LL.D., 



SUPERINTENDENT AMERICAN NAUTICAL ALMANAi. 
FORMERLY PROFESSOR AT T1IE U. B. NAVAL 0B8RVATOBY, 



WITH ONE HUNDRED AND TWELVE ENGRAVINGS, 
AND FIVE MAPS OF THE STARS. 




NEW YORK: 

HARPER & BROTHERS, PUBLISHERS, 

FRANKLIN SQUARE. 

1878. 






Entered according to Act of Congress, in the year 1877, by 

Harper & Brothers, 

In the Office of the Librarian of Congress, at Washington. 

By Exchange 
Army and Navy Club 
JANUARY 16 1934 



f>n 



PREFACE 



To prevent a possible misapprehension in scientific quar- 
ters, the author desires it understood that the present work 
is not designed either to instruct the professional investi- 
gator or to train the special student of astronomy. Its main 
object is to present the general reading public with a con- 
densed view of the history, methods, and results of astro- 
nomical research, especially in those fields which are of most 
popular and philosophic interest at the present day. couched 
in such language as to be intelligible without mathematical 
study. He hopes that the earlier chapters will, for the most 
part, be readily understood by any one having clear geomet- 
rical ideas, and that the later ones will be intelligible to all. 
To diminish the difficulty which the reader may encounter 
from the unavoidable occasional use of technical terms, a 
Glossary has been added, including, it is believed, all that 
are used in the present work, as well as a number of others 
which may be met with elsewhere. 

Respecting the general scope of the work, it may be said 
that the historic and philosophic sides of the subject have 
been treated with greater fulness than is usual in works of 
this character, while the purely technical side has been pro- 
portionately condensed. Of the four parts into which it is 
divided, the first two treat of the methods by which the mo- 



VI PREFACE. 

tions and the mutual relations of the heavenly bodies have 
been investigated, and of the results of such investigation, 
while in the last two the individual peculiarities of those 
bodies are considered in greater detail. The subject of the 
general structure and probable development of the universe, 
which, in strictness, might be considered as belonging to the 
first part, is, of necessity, treated last of all, because it re- 
quires all the light that can be thrown upon it from every 
available source. Matter admitting of presentation in tabular 
form has, for the most part, been collected in the Appendix, 
where will be found a number of brief articles for the use 
of both the general reader and the amateur astronomer. 

The author has to acknowledge the honor done him by 
several eminent astronomers in making his work more com- 
plete and interesting by their contributions. Owing to the 
great interest which now attaches to the question of the con- 
stitution of the sun, and the rapidity with which our knowl- 
edge in this direction is advancing, it was deemed desirable 
to present the latest views of the most distinguished investi- 
gators of this subject from their own pens. Four of these 
gentlemen — Eev. Father Secchi, of Home ; M. Faye, of Paris ; 
Professor Young, of Dartmouth College ; and Professor Lang- 
ley, of Allegheny Observatory — have, at the author's request, 
presented brief expositions of their theories, which will be 
found in their own language in the chapter on the sun. 

An Addendum gives the basis of the remarkable modifi- 
cation of the theory of the solar spectrum proposed by Dr. 
Henry Draper, which appeared while the sheets were passing 
through the press. 



PREFACE TO THE SECOND EDITION, 



The great favor with which this work lias been received by 
the public has led the author and publishers to give it a thor- 
ough revision, and to add the latest results of astronomical 
research. The new subjects treated comprise the results of 
Dr. Draper's discoveries in the solar spectrum, of Janssen's 
new methods of photographing the sun, and of the British 
observations of the late transit of Venus; Professor Hall's 
discovery of the satellites of Mars, and the results of recent 
investigations of the motion of the moon. Alterations and 
additions have been made wherever necessary to bring the 
work fully up to date, and several errors which crept into the 
first edition have been corrected. It is hoped that the gen- 
eral reader will now find in it the fullest practicable explana- 
tion of every branch of the subject which can interest him. 

Washington, June v 1878. 



CONTENTS. 



PART I. 

THE SYSTEM OF THE WOULD HISTORICALLY DEVELOPED 

PAGE 

I XTRODUCTION 1 



CHAPTER I. 

The Ancient Astronomy, or the Apparent Motion- of rare Heav- 
enly Bodies 7 

§1. The Celestial Sphere 7 

§2. The Diurnal Motion 9 

§3. Motion of the Sun among the Stars 13 

§ 4. Precession of the Equinoxes. — The Solar Year 1'.' 

§5. The Moon's Motion 21 

§6. Eclipses of the Sun and Moon 24 

§ 7. The Ptolemaic System 32 

§8. The Calendar 44 



CHAPTER II. 

The Copernican System, or the True Motions of the Heavenly 

Bodies 51 

§ 1. Copernicus 51 

§ 2. Obliquity of the Ecliptic ; Seasons, etc. : on the Copernican Sys- 
tem 61 

§3. Tycho Brake 66 

§4. Kepler. — His Laws of Planetary Motion 68 

§5. From Kepler to Newton 71 



X CONTENTS. 

CHAPTEK III. page 

Universal Gravitation 74 

§ 1. Newton. — Discovery of Gravitation 74 

§ 2. Gravitation of Small Masses. — Density of the Earth 81 

§3. Figure of the Earth 86 

§4. Precession of the Equinoxes , 88 

§5. The Tides 90 

§ 6. Inequalities in the Motions of the Planets produced by their 

Mutual Attraction 93 

§ 7. Relation of the Planets to the Stars 103 



PART II. 

PRACTICAL ASTRONOMY. 
Introductory Remarks 105 

CHAPTER I. 

The Telescope 108 

§ 1. The First Telescopes 108 

§2. The Achromatic Telescope 116 

§3. The Mounting of the Telescope , 120 

§4. The Reflecting Telescope 123 

§ 5. The Principal Great Reflecting Telescopes of Modern Times... 127 

§6. Great Refracting Telescopes 137 

§ 7. The Magnifying Powers of the Two Classes of Telescopes 141 

CHAPTER II. 

Application of the Telescope to Celestial Measurements 148 

§ 1. Circles of the Celestial Sphere, and their Relations to Positions 

on the Earth 148 

§2. The Meridian Circle, and its Use 154 

§3. Determination of Terrestrial Longitudes 159 

§ 4. Mean, or Clock, Time 164 



CONTENTS. XI 

CHAPTER III. PAGE 

Measuring Distances in the Heavens 167 

§ 1. Parallax in General 107 

§ 2. Measures of the Distance of the Sun \1?, 

§3. Solar Parallax from Transits of Venus 177 

§ 4. Other Methods of Determining the Sun's Distance, and their 

Results 196 

§ 5. Stellar Parallax 203 

CHAPTER IV. 
The Motion of Light 212 

CHAPTER V. 
The Spectroscope 224 



PAET III. 

THE SOLAR SYSTEM. 



CHAPTER I. 
General Structure of the Solar Ststem 235 



CHAPTER II. 

The Sun 241 

§ 1. The Photosphere 241 

§2. The Solar Spots and 'Rotation 248 

§3. Periodicity of the Spots 254 

§4. Law of Rotation of the Sun 255 

§5. The Sun's Surroundings 257 

§6. Physical Constitution of the Sun 2G4 

§ 7. Views of Distinguished Students of the Sun on the Subject of 

its Physical Constitution 271 



Xll CONTENTS. 

CHAPTER III. PAGE 

The Inner Group of Planets 289 

§ 1. The Planet Mercury , '289 

§2. The Supposed Intra-Mercurial Planets 292 

§3. The Planet Venus 295 

§4. The Earth , 304 

§5. The Moon 312 

§6. The Planet Mars 326 

§7. The Small Planets 331 

CHAPTER IV. 

The Outer Group of Planets 339 

§ 1. The Planet Jupiter 339 

§2. The Satellites of Jupiter 344 

§ 8. Saturn and its System, Physical Aspect, Belts, Rotation 346 

§4. The Rings of Saturn 349 

§5. Constitution of the Ring 357 

§6. The Satellites of Saturn 359 

§7. Uranus and its Satellites 361 

§8. Neptune and its Satellite 366 

CHAPTER V. 

Comets and Meteors 378 

§1. Aspects and Forms of Comets 373 

§ 2. Motions, Origin, and Number of Comets 377 

§3. Remarkable Comets 382 

§4. Encke's Comet, and the Resisting Medium 389 

§5. Meteors and Shooting-stars 392 

§6. Relations of Comets and Meteoroids 399 

§ 7. The Physical Constitution of Comets 406 

§8. The Zodiacal Light 413 



PAET IV. 

TEE STELLAR UNIVERSE. 
Introductory Remarks 415 



CONTENTS. xiii 

CHAPTER I. pace 

The Stars as they are Seen 418 

§ 1. Number and Orders of Stars and Nebula 418 

§2. Description of the Principal Constellations 425 

§3. New and Variable Stars 434 

§4. Double Stars 444 

§5. Clusters of Stars 44H 

§6. Nebulae 452 

§7. Proper Motions of the Stars 4<;o 



CHAPTER II. 
The SrRUCTURE of the Universe 408 

§ 1. Views of Astronomers before Herschel 4<;:» 

§2. Researches of Herschel and his Successors 47:; 

§3. Probable Arrangement of the Visible Universe 486 

§4. Do the Stars really form a System? 491 



CHAPTER III. 

The Cosmogony 499 

§1. The Modern Nebular Hypothesis 501 

§2. Progressive Changes in our System :><>7 

§3. The Sources of the Sun's Heat 513 

§4. Secular Cooling of the Earth 519 

§5. General Conclusions respecting the Nebular Hypothesis 522 

§6. The Plurality of Worlds 524 



APPENDIX. 

I. List of the Principal Great Telescopes of the World 529 

II. List of the more Remarkable Double Stars 531 

III. List of the more Interesting and Remarkable Nebuljb and 

Star Clusters 533 

IV. Periodic Comets seen at more than One Return 535 



XIV CONTENTS. 

PAGE 

V. Elements of the Orbits of the Eight Major Planets for 1850. 536 

Elements of the Satellites of Jupiter 537 

Elements of the Satellites of Saturn 537 

Elements of the Satellites of Mars 537 

Elements of the Satellites of Uranus 537 

Elements of the Satellite of Neptune 537 

VI. Elements of the Small Planets 538 

VII. Determinations of Stellar Parallax 543 

VIII. Synopsis of Papers on the Solar Parallax, 1854-77 546 

IX. List of Astronomical Works, most of which have been con- 
sulted as Authorities in the Preparation of the Present 

Work 550 

X. Glossary of Technical Terms of Frequent Occurrence in 

Astronomical Works 557 

Index 567 

Explanation of the Star Maps 572 



LIST OF ILLUSTRATIONS. 



FIG. PAGE 

The Great Telescope of the United States Naval Observato- 
ry, Washington Fronts, 

1. Section of the Imaginary Celestial Sphere 8 

2. Map illustrating the Diurnal Motion ropnd thi. Polk 10 

3. The Celestial Sphere and Diurnal Motion 12 

4. Motion of the Sun past the Star Rkoulus 1"> 

f>. Showing the Sun to re farther than the Moon 22 

G. Annular Eclipse of the Sun 86 

7. Partial Eclipse of the Sun 96 

8. Eclipse of the Sun, the Shadow of the Moon falling on the 

Earth 26 

9. Eclipse of the Moon, in the Shadow of the Earth 27 

10. Showing the Apparent Orbit of a Planet 3S 

11. Apparent Orbits of Jupiter and Saturn 39 

12. Arrangement of the Seven Planets in the Ptolemaic System... 41 

13. The Eccentric 42 

14. Showing the Astrological Division of the Seven Planets 

among the Days of the Week 46 

15. Apparent Annual Motion of the Sun explained 56 

16. Showing how the Apparent Epicyclic Motion of the Planets 

is accounted for 66 

17. Relation of the Terrestrial and Celestial Poles and Equators. 62 

18. Causes of Changes of Seasons on the Copernican System 63 

19. Enlarged View of the Earth, showing Winter in the North- 

ern Hemisphere, and Summer in the Southern 65 

20. Illustrating Kepler's First Two Laws of Planetary Motion... 69 

21. Illustrating the Fall of the Moon towards the Earth 78 

22. Baily's Apparatus for determining the Density of the Earth. 83 

23. View of Baily's Apparatus 84 

24. Diagram illustrating the Attraction of Mountains 8.~> 

25. Precession of the Equinoxes 88 



xvi LIST OF ILLUSTRATIONS. 

FIG. PAGE 

26. Attraction of the Moon tending to produce Tides 91 

27. Armillary Sphere as described by Ptolemy 107 

28. The Galilean Telescope 110 

29. Formation of an Image by a Lens Ill 

30. Great Telescope of the Seventeenth Century 114 

31. Refraction through a Compound Prism 116 

32. Section of an Achromatic Objective 117 

33. Section of Eye-piece of a Telescope 120 

34. Mode of Mounting a Telescope 121 

35. Speculum Bringing Rays to a Single Focus by Reflection 124 

36. Herschelian Telescope 125 

37. Horizontal Section of a Newtonian Telescope 125 

38. Section of the Gregorian Telescope 126 

39. Herschel's Great Telescope 129 

40. Lord Rosse's Great Telescope 132 

41. Mr. Lassell's Great Four-foot Reflector 134 

42. The New Paris Reflector 136 

43. The Great Melbourne Reflector 138 

44. Circles of the Celestial Sphere 149 

45. The Washington Transit Circle 155 

46. Spider Lines in Field of View of a Meridian Circle 156 

47. Diagram illustrating Parallax 167 

48. Diagram illustrating Parallax 168 

49. Variation of Parallax with the Altitude 169 

50. Apparent Paths of Venus across the Sun 178 

51. Venus approaching Internal Contact on the Face of the Sun. 180 

52. Internal Contact of Limb of Venus with that of the Sun.... 180 

53. The Black Drop, or Ligament 181 

54. Method of Photographing the Transit of Venus 188 

55. Artificial Transit of Venus 190 

56. Map of the Earth, showing the* Areas of Visibility of the 

Transit of 1874 193 

57. Map of the World, showing the Regions in which the Tran- 

sit of Venus will be visiblp: on December 6th, 1882 197 

58. Effect of Stellar Parallax 204 

59. Aberration of Light 214 

60. Revolving Wheel for measuring the Velocity of Light 218 

61. Illustrating Foucault's Method of measuring the Velocity 

of Light 220 

62. Course of Rays through a Spectroscope 226 



LIST OF ILLUSTRATIONS. xvii 

no. PAGE 

<;:i. Relative Size of Sun and Planets 23*; 

64. Orbits of the Planets from the Earth outward 24<) 

64a. Aspect of the Sun's Surface as Photographed ijv Janssen at 

the Observatory of Meudon 

65. Man holding Telescope, to show Sin on Screen 249 

66. Solar Spot, after Secchi 260 

67. Changes in the Aspect <>i a Solar Spoi a- ir crosses mi. S 

Disk 252 

68. Total Eclipse of the Sun, as skin at Des Moms*, I<>\\>. Au- 

gust 7th, 1869 258 

69. Specimens of Solar Protuberances, as drawn by Se< chi 

70. The Sun, with its Chromosphere and Rrd Flames, oi Juli 

23d, 1871 267 

71. Illustrating Secchi s Theory of Solar Spots 27."» 

72. Solar Spot, after Langley 

7:5. Orbits of the Four Inner Planets, illustrating the Bccmh- 

tricity of those 01 ml.lk iky and mars 289 

74. Phases of Vi-.m rs 297 

7."). Showing the Thickness of the Earth's CRUST :><).". 

76. Distribution of Auroras 

77. View of Aurora 30!» 

78. Spectrum of Two of the Great Auroras of 1871 311 

79. Relative Size of Earth and Moon 312 

80. View of Moon near thi j; vkiii: 319 

81. Lunar Crater "'Copernicus'" 321 

82. The Planet Mars on June 23d. 1875 

83. Map of Mars 328 

84. Northern Hemisphere of Mars 32'.» 

85. Southern Hemisphere of Mars 329 

85a. Apparent Orbits of the Satellites of Mars in 1877, as ob- 
served AND LAID DOWN BY PROFESSOR HALL 331 

SG. Jupiter, as seen with the Great Washington Telescope, March 

21st, 1876 339 

87. View of Jupiter, as seen in Lord Rosse's Greai Telescope, 

February 27tii, 1861 341 

88. View of Saturn and his Rings 347 

89. Specimens of Drawings of Saturn by Various Observers 351 

90. Views of Encke's Comet in 1871 37.~> 

91. Head of Donati's Great Comet of 1858. 376 

!>2. Parabolic and Elliptic Orbit of a Comet 378 



XVlll LIST OF ILLUSTRATIONS. 

FIG. PAGE 

93. Orbit of Halley's Comet 385 

94. Great Comet of 1858 388 

95. Meteor Paths, illustrating the Radiant Point 398 

96. Orbit of November Meteors and the Comet of 1861 402 

97. Orbit of the Third Comet of 1862 403 

98. Measure of Position Angle of Double Star 440 

99. Distance of Components of Double Star 446 

100. Diagram to illustrate Position Angle 446 

101. Telescopic View of the Pleiades 450 

102. Cluster of 47 Toucani 452 

103. Cluster w Centauri 452 

104. The Great Nebula of Orion 454 

105. The Annular Nebula in Lyra... 456 

106. The Omega Nebula 458 

107. Nebula Herschel 3722 459 

108. The Looped Nebula; Herschel 2941 459 

109. Herschel's View of the Porm of the Universe 477 

110. Illustrating Herschel's Orders of Distance of the Stars.... 479 

111. Probable Arrangement of the Stars and Nebula Visible 

with the Telescope 489 

112. Diagram illustrating Elliptic Elements of a Planet 560 



STAR MAPS. 

Map I. — The Northern Constellations within 50° ^ 
of the Pole 

' ; II. — Southern Constellations Visible in Au- 
tumn and Winter 

" III. — Southern Constellations Visible in Win- 
ter and Spring 

" IV. — Southern Constellations Visible in Spring 
and Summer 

" V. — Southern Constellations Visible in Sum- 
mer and Autumn J 



} At End of Book. 



POPULAR ASTRONOMY. 



PART I. — THE SYSTEM OF THE WOULD 
HISTORICALLY DEVELOPED. 



INTRODUCTION. 



Astronomy is the most ancient of the physical sciences, be- 
ing distinguished among them by its slow and progressive 
development from the earliest ages until the present time. 
In no other science has each generation which advanced it 
been so much indebted to its predecessors for both the facts 
and the ideas necessary to make the advance. The conception 
of a globular and moving earth pursuing her course throng] 1 
the celestial spaces among her sister planets, which wo see as 
stars, is one to the entire evolution of which no one mind and 
no one age can lay claim. It was the result of a gradual 
process of education, of which the subject was not an indi- 
vidual, but the human race. The great astronomers of all 
ages have built upon foundations laid by their predecessors ; 
and when we attempt to search out the tirst founder, we find 
ourselves lost in the mists of antiquity. The theory of uni- 
versal gravitation was founded by Newton upon the laws of 
Kepler, the observations and measurements of his French con- 
temporaries, and the geometry of Apollonius. Kepler used 
as his material the observations of Tycho Brahe, and built 
upon the theory of Copernicus. When we seek the origin of 
the instruments used by Tycho, we soon find ourselves among 



2 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

the mediaeval Arabs. The discovery of the true system of 
the world by Copernicus was only possible by a careful study 
of the laws of apparent motion of the planets as expressed in 
the epicycles of Ptolemy and Hipparchus. Indeed, the more 
carefully one studies the great work of Copernicus, the more 
surprised he will be to find how completely Ptolemy furnished 
him both ideas and material. If we seek the teachers and 
predecessors of Hipparchus, we find only the shadowy forms 
of Egyptian and Babylonian priests, whose names and writings 
are all entirely lost. In the earliest historic ages, men knew 
tliat the earth was round ; that the sun appeared to make an 
annual revolution among the stars; and that eclipses were 
caused by the moon entering the shadow of the earth, or the 
earth that of the moon. 

Indeed, each of the great civilizations of the ancient world 
seems to have had its own system of astronomy strongly 
marked by the peculiar character of the people among whom 
it was found. Several events recorded in the annals of China 
show that the movements of the sun and the laws of eclipses 
were studied in that country at a very early age. Some of 
these events must be entirely mythical ; as, for instance, the 
despatch of astronomers to the four points of the compass for 
the purpose of determining the equinoxes and solstices. But 
there is another event which, even if we place it in the same 
category, must be regarded as indicating a considerable amount 
of astronomical knowledge among the ancient Chinese. We 
refer to the tragic fate of Hi and Ho, astronomers roval to one 
of the ancient emperors of that people. It was part of the 
duty of these men to carefully study the heavenly movements, 
and give timely warning of the approach of an eclipse or other 
remarkable phenomenon. But, neglecting this duty, they gave 
themselves up to drunkenness and riotous living. In conse- 
quence, an eclipse of the sun occurred without any notice being 
given ; the religious rites due in such a case were not performed, 
and China was exposed to the anger of the gods. To appease 
their wrath, the unworthy astronomers were seized and sum- 
marily executed by royal command. Some historians have 



INTIiODUCTKjy. 3 

gone so far as to fix the date of this occurrence, which is vari- 
ously placed at from 2128 to 2159 years before the Christian 
era. If this is correct, it is the earliest of which profane his- 
tory lias left us any record. 

In the Hindoo astronomy we see the peculiarities of the 
contemplative Hindoo mind strongly reflected. Here the 
imagination revels in periods of time which, by comparison, 
dwarf even the measures of the celestial spaces made by mod- 
ern astronomers. In this, and in perhaps other ancient - 
terns, we find references to a supposed conjunction of all the 
planets 3102 years before the Christian era. Although we 
have every reason for believing that this conjunction was 
learned, not from any actual record of it, but by calculating 
back the position of the planets, yet the very fact that they 
were able to make this calculation shows that the motions of 
the planets must have been observed and recorded during 
many generations, either by the Hindoos themselves, or some 
other people from whom they acquired their knowledge. A- 
a matter of fact, we now know from our modern tables that 
this conjunction was very far from being exact ; bat its error 
could not be certainly detected by the rude observations of the 
times in question. 

Among a people so prone as the ancient Greeks to speculate 
upon the origin and nature of things, while neglecting the ob- 
servation of natural phenomena, we cannot expect to find any- 
thing that can be considered a system of astronomy. But there 
are some ideas attributed to Pythagoras which are so frequent- 
ly alluded to, and so closely connected witli the astronomy of 
a subsequent age, that we may give them a passing mention. 
He is said to have taught that the heavenly bodies were set 
in a number of crystalline spheres, in the common centre of 
which the earth was placed. In the outer of these spheres 
were set the thousands of fixed stars which stud the firma- 
ment, while each of the seven planets had its own sphere. The 
transparency of each crystal sphere was perfect, so that the 
bodies set in each of the outer spheres were visible through 
all the inner ones. These spheres all rolled round on each 



4 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

other in a daily revolution, thus causing the rising and setting 
of the heavenly bodies. This rolling of the spheres on each 
other made a celestial music, the " music of the spheres," 
which filled the firmament, but was of too elevated a char- 
acter to be heard by the ears of mortals. 

It must be admitted that the idea of the stars being set in a 
hollow sphere of crystal, forming the vault of the firmament, 
was a very natural one. They seemed to revolve around the 
earth every day, for generation after generation, without the 
slightest change in their relative positions. If there were no 
solid connection between them, it does not seem possible that 
a thousand bodies could move around their vast circuit for 
such long periods of. time without a single one of them vary- 
ing its distance from one of the others. It is especially diffi- 
cult to conceive how they could all move around the same 
axis. But when they are all set in a solid sphere, every one is 
made secure in its place. The planets could not be set in the 
same sphere, because they change their positions among the 
stars. This idea of the sphericity of the heavens held on to 
the minds of men with remarkable tenacity. The funda- 
mental proposition of the system, both of Ptolemy and Coper- 
nicus, was that the universe is spherical, the latter seeking to 
prove the naturalness of the spherical form by the analogy 
of a drop of water, although the theory served him no pur- 
pose whatever. Faint traces of the idea are seen here and 
there in Kepler, with whom it vanished from the mind of the 
race, as the image of Santa Clans disappears from the mind of 
the growing child. 

Pythagoras is also said to have taught in his esoteric lect- 
ures that the sun was the real centre of the celestial move- 
ments, and that the earth and planets moved around it, and it 
is this anticipation of the Copernican system which constitutes 
his greatest glory. But he never thought proper to make a 
public avowal of this doctrine, and even presented it to his 
disciples somewhat in the form of an hypothesis. It must 
also be admitted that the accounts of his system which have 
reached us are so vague and so filled with metaphysical specu- 






INTRODUCTION. 5 

lation that it is questionable whether the frequent application 

of liis name to the modern system is not more pedantic than 
justifiable. 

The Greek astronomers of a later age not only rejected the 
vague speculations of their ancestors, but proved them-elves 
the most careful observers of their time, and first made astron- 
omy worthy the name of a science. From this Greek astrono- 
my the astronomy of our own time may be considered as com- 
ing by direct descent. Still, were it not for the absence of his- 
toric records, we could probably trace back both their theories 
and their system of observation to the plains of Chaldea. The 
zodiac was mapped out and the constellations named many 
centuries before they commenced their observation.-, and tl 
works marked quite an advanced stage of development. This 
prehistoric knowledge is, however, to be treated by the histo- 
rian rather than the astronomer. If we confine ourselves to 
men whose names and whose labors have come down to us. 
we must concede to Ilipparchus the honor of being the father 
of astronomy. Not only do his observations of the heavenly 
bodies appear to have been far more accurate than those of 
any of his predecessors, but he also determined the laws of the 
apparent motions of the planets, and prepared tables by which 
these motions could be calculated. Probably he was the first 
propounder of the theory of epicyclic motions of the planets, 
commonly called after the name of his successor, Ptolemy, who 
lived three centuries later. 

Commencing with the time of Ilipparchus, the general 
theory of the structure of the universe, or "system of the 
world," as it is frequently called, exhibits three great stages of 
development, each stage being marked by a system quite dif- 
ferent from the other two in its fundamental principles. These 
are : 

1. The so-called Ptolemaic system, which, however, really 
belongs to Ilipparchus, or some more ancient astronomer. In 
this system the motion of the earth is ignored, and the appar- 
ent motions of the stars and planets around it are all regarded 
as real. 



6 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

2. The Copernican system, in which it is shown that the sun 
is really the centre of the planetary motions, and that the earth 
is itself a planet, both turning on its axis and revolving round 
the sun. 

3. The Newtonian system, in which all the celestial motions 
are explained by the one law of universal gravitation. 

This natural order of development shows the order in which 
a knowledge of the structure of the universe can be most 
clearly presented to the mind of the general reader. We 
shall therefore explain this structure historically, devoting a 
separate chapter to each of the three stages of development 
which we have described. We commence with what is well 
known, or, at least, easily seen by every one who will look at 
the heavens with sufficient care. We imagine the observer 
out-of-doors on a starlit night, and show him how the heav- 
enly bodies seem to move from hour to hour. Then, we show 
him what changes he will see in their aspects if he contin- 
ues his watch through months and years. By combining the 
apparent motions thus learned, he forms for himself the an- 
cient, or Ptolemaic, system of the world. Having this system 
clearly in mind, the passage to that of Copernicus is but a 
step. It consists only in showing that certain singular oscilla- 
tions which the sun and planets seem to have in common are 
really due to a revolution of the earth around the sun, and 
that the apparent daily revolution of the celestial sphere arises 
from a rotation of the earth on its own axis. The laws of 
the true motions of the planets being perfected by Kepler, 
they are shown by Newton to be included in the one law of 
gravitation towards the sun. Such is the course of thought to 
which we first invite the reader. 



THE CELESTIAL SPHERE. 



CHAPTER I. 

THE ANCIENT ASTRONOMY, OR THE APPARENT MOTIONS OF THE 
HEAVENLY BODIES. 

§ 1. The Celestial Sj)hcre. 

It is a fact with which we are familiar from infancy, thai 
all the heavenly bodies — sun, moon, and stars — seem to be 
in an azure vault, which, rising high over our heads, corvee 
down to the horizon on every side. Here the earth, on which 
it seems to rest, prevents our tracing it farther. But if the 
earth were out of the way, or were perfectly transparent, we 
could trace the vault downwards on every side to the point 
beneath our feet, and could see sun, moon, and stars in every 
direction. The celestial vault above us, with the correspond- 
ing one below us, would then form a complete sphere, in the 
centre of which the observer would seem to be placed. This 
has been known in all ages as the celestial sphere. The direc- 
tions or apparent positions of the heavenly bodies, as well as 
their apparent motions, have always been defined by their sit- 
uation and motions on this sphere. The fact that it is purely 
imaginary does not diminish its value as enabling us to form 
distinct ideas of the directions of the heavenly bodies from us. 

It matters not how large we suppose this sphere, so long as 
we always suppose the observer to be in the centre of i: 
that it shall surround him on all sides at an equal distance. 
But in the language and reasoning of exact astronomv it is 
always supposed to be infinite, as then the observer may con- 
ceive of himself as transported to any other point, even to one 
of the heavenly bodies themselves, and still be, for all practical 
purposes, in the centre of the sphere. In this case, however, 
the heavenlv bodies are not considered as attached to the cir- 



8 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

cumference of the infinite sphere, but only as lying on the line 
of sight extending from the observer to some point of the 
sphere. Their relation to it may be easily understood by the 
observer conceiving himself to be luminous, and to throw out 
rays in every direction to the infinitely distant sphere. Then 
the apparent positions of the various heavenly bodies will be 
those in which their shadows strike the sphere. For instance, 
the observer standing on the earth and looking at the moon, 




Fig. 1.— Section of the imaginary celestial sphere. The observer at 0, looking at the 
stars or other bodies, marked p, q, r, s, t, w, v, will imagine them situated at P, Q, R, S, 
T, U, V, on the surface of the sphere, where they will appear projected along the 
straight pP, qQ, etc. 

the shadow of the latter will strike the sphere at a point on a 
straight line drawn from the observer's eye through the centre 
of the moon, and continued till it meets the sphere. The point 
of meeting will represent the position of the moon as seen by 
the observer. Now, suppose the latter transported to the moon. 
Then, looking back at the earth, he will see it projected on the 
sphere in a point diametrically opposite to that in which he 
formerly saw the moon. To whatever planet he might trans- 



THE DIURNAL MOTION. 9 

port himself, he would see the earth and the other planets pro- 
jected on this imaginary sphere precisely as we always seem 
to see the heavenly bodies so projected. 

This is all that is left of the old crystalline spheres of Py- 
thagoras by modern astronomy. From being a solid which 
held all the stars, the sphere has become entirely immaterial, 
a mere conception of the mind, to enable it to define the di- 
rections in which the heavenly bodies arc Been. By examin- 
ing the figure it will be clear that all bodies which lie in the 
same straight line from the observer will appear on the sam<' 
point of the sphere. For instance, bodies at the three points 
marked t will all be seen as if they were at T. 

§ 2. The Diurnal Motion. 

If we watch the heavenly bodies for a few hours we shall 
always find them in motion, those in the east rising upwards, 
those in the south moving towards the west, and th<»e in the 
west sinking below the horizon. We know that this motion 
is only apparent, arising from the rotation of the earth on it- 
axis; but as we wish, in this chapter, only t«> describe thil 
as they appear, we may speak of the motion as real. A few 
days' watching will show that the whole celestial sphere seems 
to revolve, as on an axis, every day. It is to this revolution, 
carrying the sun alternately above and below the horizon, that 
the alternations of day and night are due. The nature and 
effects of this motion can best be studied by watching the ap- 
parent movement of the stars at night. AVe should soon learn 
from such a watch that there is one point in the heavens, or 
on the celestial sphere, which does not move at all. In our 
latitudes this point is situated in the north, between the zenith 
and the horizon, and is called the pole. Around this pole, as 
a fixed centre, all the heavenly bodies seem to revolve, each 
one moving in a circle, the size of which depends on the dis- 
tance of the body from the pole. There is no star situated 
exactly at the pole, but there is one which, being situated lit- 
tle more than a degree distant, describes so small a circle that 
the unaided eye cannot see any change of place without mak- 



10 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

ing some exact and careful observation. This is therefore 
called the pole star. The pole star can nearly always be very 
readily found by means of the pointers, two stars of the con- 
stellation Ursa Major, the Great Bear, or, as it is familiarly 
called, the Dipper. By referring to the figure, the reader will 
readily find this constellation, by the dotted line from the pole 
and thence the pole star, which is near the centre of the map. 




Fig. 2.— Map of the principal stars of the northern sky, showing the constellations which 
never set in latitude 40°, but revolve round the pole star every day in the direction 
shown by the arrows. The two lower stars of Ursa Major, on the left of the map, 
point to the pole etar in the centre. 

The altitude of the pole is equal to the latitude of the place. 
In the Middle States the latitude is generally not far from 
forty degrees ; the pole is therefore a little nearer to the hori- 
zon than to the zenith. In Maine and Canada it is about half- 
way between these points, while in England and Northern 
Europe it is nearer the zenith. 



THE DIURNAL MOTION. 11 

Now, to see the effect of the diurnal motion near the pole, 
let us watch any star in the north between the pole and the 
horizon. We shall soon see that, instead of moving from i 
to west, as we are accustomed to see the heavenly bodies move, 
it really moves towards the east. After passing the north 
point, it begins to curve its course upwards, until, in the north- 
east, its motion is vertical. Then it turns gradually to the 
west, passing as far above the pole as it did below it, and, sink- 
ing down on the west of the pole, it again passes under it. 
The passage above the pole is called the upper culmination, 
and that below it the lower one. The cour>e around the pole 
is shown by the arrows on Fig. 2. We cannot with the naked 
eye follow it all the way round, on account of the intervention 
of daylight; but by continuing our watch every clear night for 
a year, we should see it in every point of its course. A star 
following the course we have described never Bets, but may be 
seen every clear night. If we imagine a circle drawn round 
the pole at such a distance as just to touch the horizon, all the 
stars situated within this circle will move in this way; this is 
therefore called the circle of perpetual apparition. 

As we go away from the pule we shall rind the stars mov- 
ing in larger circles, passing higher up over the pole, and lower 
down below it, until we reach the circle of perpetual appari- 
tion, when they will just graze the horizon. Outside this circle 
every star must dip below the horizon for a greater or less 
time, depending on its distance. If it be only a few degrees 
outside, it will set in the north-west, or between north and 
north-west ; and, after a few hours only, it will be seen to rise 
again between north and north-east, having done little more 
than graze the horizon. The possibility of a body rising so 
soon after having set does not always occur to those who live 
in moderate latitudes. In July, 1S74, Coggias comet set in 
the north-west about nine o'clock in the evening, and rose 
again about three o'clock in the morning; and some intelligent 
people who then saw it east of the pole supposed it could not 
be the same one that had set the evening before. 

Passing outside the circle of perpetual apparition, we find 



12 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 



that the stars pass south of the zenith at their upper culmina- 
tion, that they set more quickly, and that they are a longer 
time below the horizon. This may be seen in Fig. 3, the por- 
tion of the sphere to which we refer being between the celes- 
tial equator and the line LN. When we reach the equator 
one-half the course will be above and one-half below the hori- 




Fig. 3.— The celestial sphere and diurnal motion. <S is the south horizon, N the north hori- 
zon, Z the zenith. The circle LN around the north pole contains the stars shown in 
Fig. 2 ; and the observer at 0, in the centre of the sphere, looking to the north, sees the 
stars as they are depicted in that figure. The arrows show the direction of the diurnal 
motion in the west. 

zon. South of the equator the circles described by the stars 
become smaller once more, and more than half their course is 
below the horizon. Near the south horizon the stars only show 
themselves above the horizon for a short time, while below it 
there is a circle of perpetual disappearance, the stars in which, 
to us, never rise at all. This circle is of the same magnitude 



MOTION OF THE SUN AM OX a THE STARS. 13 

with that of perpetual apparition, and the south pole is situated 
in its centre, just as the north pole is in the centre of the other. 

If we travel southward we find that the north pole gradually 
sinks towards the horizon, while new stars come into view above 
the south horizon ; consequently the circles of perpetual appari- 
tion and of perpetual disappearance both grow smaller. When 
we reach the earth's equator the south pole has risen to the 
south horizon, the north pole has sunk to the north hori- 
zon ; the celestial equator passes from east to west directly 
overhead; and all the heavenly bodies in their diurnal revolu- 
tions describe circles of which one half is above and the other 
half below the horizon. These circles are all vertical. 

South of the equator only the south pole is visible, the north 
one, which we see, being now below the horizon. Beyond the 
southern tropic the sun is north at noon, and, instead of mov- 
ing from left to right, its course is from right to left. 

The laws of the diurnal motion which we have described 
may be summed up as follows: 

1. The celestial sphere, with the sun, moon, and stars, seems 
to revolve daily around an inclined axis passing through the 
point where we may chance to stftnd. 

2. The upper end of this axis points (in this hemisphere) to 
the north pole; the other end passes into the earth, and points 
to the south pole, which is diametrically opposite, and therefore 
below the horizon. 

3. All the iixed stars during this revolution move together, 
keeping at the same distance from each other, as if the revolv- 
ing celestial sphere were solid, and they were set in it. 

4. The circle drawn round the heavens half-way between 
the two poles being the celestial equator, all bodies north of 
this equator perform more than half their revolution above 
the horizon, while south of it less than half is above it. 

§ 3. Motion of the Sun among the Stars. 

The most obvious classification of the heavenly bodies which 
we see with the naked eye is that of sun, moon, and stars. 
liut there is also this difference among the stars, that while the 



14 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

great mass of them preserve the same relative position on the 
celestial sphere, year after year and century after century, there 
are five which constantly change their positions relatively to 
the others. Their names are Mercury, Yenus, Mars, Jupiter, 
and Saturn. These five, with the sun and moon, constitute the 
seven planets, or wandering stars, of the ancients, the motions 
of which are next to be described. Taking out the seven 
planets, the remaining heavenly bodies visible to the naked 
eye are termed the Fixed Stars, because they have no appar- 
ent motion, except the regular diurnal revolution described in 
the last section. But if we note the positions of the sun, 
moon, and planets among the stars for a number of successive 
nights, we shall find certain slow changes among them which 
we shall now describe, beginning with the sun. In studying 
this description, the reader must remember that we are not 
seeking for the apparent diurnal motion, but only certain 
much slower motions of the planets relative to the fixed stars, 
such as would be seen if the earth did not rotate on its axis. 

If we observe, night after night, the exact hour and minute 
at which a star passes any point by its diurnal revolution, we 
shall find that passage to *occur some four minutes earlier 
every evening than it did the evening before. The starry 
sphere therefore revolves, not in 24 hours, but in 23 hours 
56 minutes. In consequence, if we note its position at the 
same hour night after night, we shall find it to be farther and 
farther to the west. Let us take, for example, the brightest 
star in the constellation Leo, represented on Map III., and 
commonly known as Regulus. If we watch it on the 22d of 
March, we shall find that it passes the meridian at ten o'clock 
in the evening. On April 22d it passes at eight o'clock, and 
at ten it is two hours west of the meridian. On the same day 
of May it passes at six, before sunset, so that it cannot be seen 
on the meridian at all. When it first becomes visible in the 
evening twilight, it will be an hour or more west of the me- 
ridian. In June it will be three hours west, and by the end of 
July it will set during twilight, and will soon be entirely lost 
in the rays of the sun. This shows that during the months in 



MOTIOX OF THE 8UX AMONG THE STABS. 15 

question the sun has been approaching the star from the west, 
and in August has got so near it that it is no longer visible. 

Carrying forward our computation, we rind that on Angnst 
21st the star crosses the meridian at noon, and therefore at 
nearly the same time with the sun. In September it crosses 
at ten in the morning, while the sun is on the eastern side. 
The sun has therefore passed from the west to the east of the 
star, and the latter can be seen rising in the morning twilight 
before the sun. It constantly rises earlier and earlier, and 
therefore farther from the sun, until February, when it 1 
at sunset and sets at sunrise; and is therefore directly opposite 
the sun. In March the star would cross the meridian at ten 
o'clock once more, showing that in the course of a year the 
sun and star had resumed their first position. But, while the 
sun has risen and set 365 times, the star has risen and set 366 
times, the sun having lost an entire revolution by the slow 
backward motion we have described. 

If the stars were visible in the daytime (as they would be 
but for the atmosphere), the apparent motion of the sun among 
them could be seen in the course of a single day. For in- 
stance, if we could have seen Eegulus rise on the morning of 
August 20th, 1876, we should have seen the sun a little south 
and west of it, the relative position of the sun being as shown 
by the circle numbered 1 in the figure. „. 

Watching the star all day, we should find OOTY^) 

that at sunset it was north from the sun, 1321 

as from circle No. 2. The sun would ^T^'ZZ 
during the day have moved nearly its own about August aetu of 
diameter. Next morning: we should have 
seen that the sun had gone past the star into position 3, so 
that the latter would now rise before the former. By sun- 
set it would have advanced to position 4, and so forth. The 
path which the sun describes among the stars in his annual 
revolution is called the ecliptic. It is marked down on Maps 
II., III., IV., and V., and the months in which the sun passes 
through each portion of the ecliptic are also indicated. A 
belt of the heavens, extending a few degrees on each side of 

3 



16 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 

the ecliptic, is called the zodiac. The poles of the ecliptic are 
two opposite points, each in the centre of one of the two hemi- 
spheres into which the ecliptic divides the celestial sphere. 

The determination of the solar motion around the ecliptic 
may be considered the birth of astronomical science. The 
prehistoric astronomers divided the ecliptic and zodiac into 
twelve parts, now familiarly known as the signs of the zodiac. 
This proceeding w T as probably suggested by the needs of agri- 
culture, and of the chronological reckoning of years. A very 
little observation would show that the changes of the seasons 
are due to the variations in the meridian altitude of the sun, 
and in the length of the day ; but it was only by a careful 
study of the position of the ecliptic, and the motion of the sun 
in it, that it could be learned how these variations in the daily 
course of the sun were brought about. This study showed 
that they were due to the fact that the ecliptic and equator 
did not coincide, but were inclined to each other at an angle 
of between twenty-three and twenty-four degrees. This in- 
clination is known as the obliquity of the ecliptic. The two 
circles, equator and ecliptic, cross each other at two opposite 
points, the positions of which among the stars may be seen by 
reference to Maps II. -V. When the sun is at either of 
these points, it rises exactly in the east, and sets exactly in the 
west ; one-half its diurnal course is above the horizon, and the 
other half below. The days and nights are therefore of equal 
length, from which the two points in question are called the 
Equinoxes. 

The vernal equinox is on the right-hand edge of Map II. 
Leaving that equinox about March 21st, the sun crosses over 
the region represented by the map in the course of the next 
three months, working northward as it does so, until June 20th, 
when it is on the left-hand edge of the map, 23^° north of the 
equator. This point of the ecliptic is called the summer solstice, 
being that in which the snn attains its greatest northern declina- 
tion. When near, this solstice, it rises north of east, culmi- 
nates at a high altitude (in our latitudes), and sets north of 
west. As explained in describing the diurnal motion of an 



MOTION OF THE SUN AMONG THE STARS. 17 

object north of the celestial equator, more than half the daily 
course of the sun is now above our horizon, so that our days 
are longer than our nights, while the great meridian altitude 
of the sun produces the heats of summer. 

The portion of the ecliptic represented on 'Map II., com- 
mencing at the vernal equinox, where the sun crosses the equa- 
tor, was divided by the early astronomers into the three signs 
of Aries, the Ram ; Taurus, the Bull ; and Gemini, the Twins. 
It will be seen that these signs no longer coincide with the 
constellations of the same name : this is owing to a change in 
the position of the equator, which will be described presently. 

Turning to Map III., we see that during the three months. 
from June to September, the sun works downwards towards 
the equator, reaching it about September 20th. The point of 
crossing marks the autumnal equinox, found also on the right 
hand of Map IV. The days and nights are now once more of 
equal length. 

During the next six months the sun is passing over the re- 
gions represented on Maps IV. and V., and is south of the 
equator, its greatest southern declination, or "the southern 
solstice," being reached about December 21st. More than 
half its daily course is then below the horizon, so that in our 
latitudes the nights are longer than the davs, and the low 
noonday altitude of the sun gives rise to the colds of winter. 

We have no historic record of this division of the zodiac 
into signs, and the ideas of the authors can only be inferred 
from collateral circumstances. It has been fancied that the 
names were suggested by the seasons, the agricultural opera- 
tions, and so on. Thus the spring signs (Aries, the Ram : Tau- 
rus, the Bull; and Gemini, the Twins) are supposed to mark the 
bringing forth of young by the flocks and herds. Cancer, the 
Crab, marks the time when the sun, having attained its great- 
est declination, begins to go back towards the equator; and the 
crab having been supposed to move backwards, his name was 
given to this sign. Leo, the Lion, symbolizes the fierce heat 
of summer; and Virgo, the Virgin, gleaning corn, symbolizes 
the harvest. In Libra, the Balance, the day and night balance 



18 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

each other, being of equal length. Scorpius, the Scorpion, is 
supposed to have marked the presence of venomous reptiles in 
October ; while Sagittarius, the Archer, symbolizes the season 
of hunting. The explanation of Capricorn us, the Goat, is more 
fanciful, if possible, than that of Cancer. It was supposed that 
this animal, ascending the hill as he feeds, in order to reach 
the grass more easily, on reaching the top, turns back again, so 
that his name was used to mark the sign in which the sun, 
from going south, begins to return to the north. Aquarius, 
the Water-bearer, symbolizes the winter rains; and Pisces, the 
Fishes, the season of fishes. 

All this is, however, mere conjecture; the only coincidences 
at all striking being Yirgo and Libra. The names of the con- 
stellations were probably given to them several centuries, per- 
haps even thousands pf years, before the Christian era ; and in 
that case the zodiacal constellations would not have correspond- 
ed to the seasons we have indicated. An attempt has even been 
made to show that the names of the zodiacal constellations were 
intended to commemorate the twelve labors of Hercules; but 
this theory rests on no better foundation than the other. 

The zodiacal constellations occupy quite unequal spaces in 
the heavens, as may be seen by inspection of the maps. In 
the beginning they were simply twelve houses for the sun, 
which that luminary occupied in the course of the year. Hip- 
parchus found this system entirely insufficient for exact astron- 
omy, and therefore divided the ecliptic and zodiac into twelve 
equal parts, of 30° each, called signs of the zodiac. lie gave 
to these signs the names of the constellations most nearly cor- 
responding to them. Commencing at the vernal equinox, the 
first arc of 30° was called the sign Aries, the second the sign 
Taurus, and so forth. The mode of reckoning positions on 
the ecliptic by signs was continued until the last century, but 
is no longer in use among professional astronomers, owing to 
its inconvenience. The whole ecliptic is now divided into 
360°, like any other circle, the count commencing at the vernal 
equinox, and following the direction of the sun's motion all the 
way round to 360°. 



PRECESSION OF THE EQUINOXES. 19 

§ 4. Precession of the Equinoxes. — The Solar Year. 
By comparing his own observations with those of preceding 
astronomers, Hipparchus found that the equinoxes were slowly 
shifting their places among the stars, the change being at least 
a degree in a century towards the west. His successors deter- 
mined it with greater exactness, and it is now known to be 
nearly a degree in seventy years. Careful study of the change 
shows that it is due mainly to a motion of the equator, which 
again arises from a change in the direction of the pole. The 
position of the ecliptic among the stars varies so slowly that the 
change can be seen only by the refined observations of modern 
times. In the explanation of the diurnal motion, it was stated 
that there was a certain point in the heavens around which all 
the heavenly bodies seem to perform a daily revolution. This 
point, the pole of the heavens, is marked on the centre of Map 
I., and is also in the centre of Fig. 2, page 10. It is little more 
than a degree distant from the pole star. Now, precession real- 
ly consists in a very slow motion of this pole around the pole 
of the ecliptic, the rate of motion being such as to carry it all 
the way round in about 25,300 years. The exact time has 
never been calculated, and would not always be the same, ow- 
ing to some small variations to which the motion is subject ; 
but it will never differ much from this. There is a very slight 
motion to the ecliptic itself, and therefore to its pole ; and this 
fact renders the motion of the pole of the equator around it 
somewhat complicated ; but the curve described b} T the latter 
is very nearly a circle 46° in diameter. In the time of Hip- 
parchus, our present pole star was 12° from the pole. The pole 
has been approaching it steadily ever since, and will continue 
to approach it till about the year 2100, when it will slowly 
pass by it at the distance of less than half a degree. The 
course of the pole during the next 12,000 years is laid down 
on the map, and it will be seen that at the end of that time 
it will be near the constellation Lyra. Since the equator is 
always 90° distant from the pole, there will be a correspond- 
ing motion to it, and hence to the point of its crossing the 



20 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

ecliptic. To show this, the position of the equator 2000 years 
ago, as well, as its present position, is given on Map II. 

The reader will, of course, understand that the various ce- 
lestial movements of which we have spoken in this chapter are 
only apparent motions, and are due to the motion of the earth 
itself, as will be explained in the chapter on the Copernican 
system. The diurnal revolution of the celestial sphere is due 
to the rotation of the earth on its axis, while precession is real- 
ly a change in the direction of that axis. 

One important effect of precession is that one revolution of 
the sun among the stars does not accurately correspond to the 
return of the same seasons. The latter depend upon the posi- 
tion of the sun relative to the equinox, the time when the sun 
crosses the equator towards the north always marking the sea- 
son of spring (in the northern hemisphere), no matter where 
the sun may be among the stars. If the equator did not move, 
the sun would always cross it at nearly the same point among 
the stars. But when, starting from the vernal equinox, it 
makes the circuit of the heavens, and returns to it again, the 
motion of the equator has been such that the sun crosses it 
20 minutes before it reaches the same star. In one year, tin's 
difference is very small ; but by its constant accumulation, at 
the rate of 20 minutes a year, it becomes very considerable 
after the lapse of centuries. We must, therefore, distinguish 
between the sidereal and the tropical year, the former being 
the period required for one revolution of the sun among the 
stars, the latter that required for his return to the same equi- 
nox, whence it is also called the equinoctial year. The exact 
lengths of these respective years are : 

Days. Days. Hours. Min. Sec. 

Sidereal year 365.25636 = 365 6 9 9 

Tropical year 365.24220 = 365 5 48 46 

Since the recurrence of the seasons depends on the tropical 
year, the latter is the one to be used in forming the calendar, 
and for the purposes of civil life generally. Its true length is 
11 minutes 14 seconds less than 365J days. Some results of 
this difference will be shown in explaining the calendar. 



THE MOON. 21 

§ 5. The Moon's Motion. 

Every one knows that the moon makes a revolution in the 
celestial sphere in about a month, and that during its revolu- 
tion it presents a number of different phases, known as u new 
moon," " first quarter," " full moon," and so on, depending 
on its position relative to the sun. A study of these phases 
during a single revolution will make it clear that the moon is 
a globular dark body, illuminated by the light of the sun, a 
fact which has been evident to careful observers from the re- 
motest antiquity. This may be illustrated by taking a large 
globe to represent the moon, painting one half white, to rep- 
resent the half on which the sun shines, and the other half 
dark. Viewing it at a proper distance, and turning it into 
different positions, it will be found that the visible part of the 
white half may be made to imitate the various appearances of 
the moon. 

As the sun makes a revolution around the celestial sphere 
in a year, so the moon makes a similar revolution among the 
stars in a little more than 27 days. This motion can be seen 
on any clear night between first quarter and full moon, if the 
moon happens to be near a bright star. If the position of the 
moon relatively to the star be noted from hour to hour, it will 
be found that she is constantly working towards the east by a 
distance equal to her own diameter in an hour. The follow- 
ing night she will be found from 12° to 14° east of the star, 
and will rise, cross the meridian, and set from half an hour to 
an hour later than she did the preceding night. At the end 
of 27 days 8 hours, she will be back in the same position 
among the stars in which she was first seen. 

If, however, starting from one new moon, we count forwards 
this period, we shall find that the moon, although she has re- 
turned to the same position among the stars, has not got back 
to new moon again. The reason is that the sun has moved 
forwards, in virtue of his apparent annual motion, so far that 
it will require more than two days for the moon to overtake 
him. So, although the moon really revolves around the earth 



22 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

in 27^ days, the average interval between one new moon and 
the next is 29-J days. 

A comparison of the phases of the moon with her direction 
will show that the sun is many times more distant than the 
moon. In Fig. 5, let E be the position of an observer on the 
earth, M the moon, and S the sun, illuminating one half of it. 
When the observer sees the moon in her first quarter — that is, 
when her disk appears exactly half illuminated — the angle at 



Fig. 5 — Showing the sun to be farther than the moon. 

the moon, between the observer and the sun, must be a right 
angle. If the sun were only about four times as far as the 
moon, as in the figure, the observer, by measuring the angle 
SEM between the sun and moon, would find it to be 75° ; and 
the nearer the sun, the smaller he would find it. But actual 
measurement would show it to be so near 90° that the dif- 
ference would be imperceptible with ordinary instruments. 
Hence, the sun is really at the point where the dotted line and 
the line MS continued meet each other, which is many times 
the distance EM to the moon. 

This idea was applied by Aristarchus, who flourished in the 
third century before Christ, preceding both Hipparchus and 
Ptolemy, to determine the distance of the sun, or, more ex- 
actly, how many times it exceeded the distance of the moon. 
He found, by measurement, that, in the position represented 
in the figure, the distance between the directions of the sun 
and moon was 87°,. and that the sun was therefore something 
like twenty times as far as the moon. We now know that this 
result was twenty times too small, the angle being really so 
near 90° that Aristarchus could not determine the difference 
with certainty. In principle, the method is quite correct, and 



THE MOON. 23 

very ingenious, but it cannot be applied in practice. The one 
insuperable difficulty of the method arises from the impossi- 
bility of seeing when the moon is exactly half illuminated, 
the uncertainty arising from the inequalities in the lunar sur- 
face being greater than the whole angle to be measured. 

Watching and mapping down the path of the moon among 
the stars, it is found not to be the same with that of the sun, 
being inclined to it about 5°. The paths cross each other in 
two opposite points of the heavens, called the moon's nodes. 
The path of the moon in the middle of the year 1877 is 
marked on star Maps II.- V. Referring to Map III., it will 
be seen that the descending node of the moon is in the con- 
stellation Leo, very near the star Regulus. Here the moon 
passes south of or below the ecliptic, and continues below it 
over the whole of Map IV. On Map V., it approaches the 
ecliptic again, crossing to the north of it in the constellation 
Aquarius, and continuing on that side till it reaches Regulus 
once more. 

Such is the moon's path in July, 1S77. But it is con- 
stantly changing in consequence of a motion of the nodes 
towards the west, amounting to more than a degree in every 
revolution. In order that the line drawn on the map may 
continue to represent the path of the moon, we must suppose 
it to slide along the ecliptic towards the right at the rate of 
about 20° a year, so that a slightly different path will be de- 
scribed in every monthly revolution. The path will always 
cross the ecliptic at the same angle, but the moon will not 
always pass over the same stars. In August, 1S77, she will 
cross the ecliptic a little farther to the right (west), and will 
pass a little below Regulus. The change going on from 
month to month and from year to year, in a little less than 
ten years the ascending node will be found in Leo ; and the 
other node, now in Leo, will have gone back to Aquarius. 
In a period of eighteen years and seven months, the nodes 
will have made a complete revolution, and the path of the 
moon will have resumed the position given on the map. 



24 SYSTEM OF TEE WORLD HISTORICALLY DEVELOPED. 

. § 8. Eclipses of the Sun and Moon. 

The early inhabitants of the world were, no doubt, terrified 
by the occasional recurrence of eclipses many ages before 
there were astronomers to explain their causes. But the mo- 
tions of the sun and moon could not be observed very long 
without the causes being seen. It was evident that if the 
moon should ever chance to pass between the earth and the 
sun, she must cut off some or all of his light. If the two bodies 
followed the same track in the heavens, there would be an 
eclipse of the sun every new moon ; but, owing to the incli- 
nation of the two orbits, the moon will generally pass above 
or below the sun, and there will be no eclipse. If, however, 
the sun happens to be in the neighborhood of the moon's node 
when the moon passes, then there will be an eclipse. For an 
example, let us refer to Map III. We see that the sun passes 
the moon's descending node about August 25th, 1877, and is 
within 20° of this node from early in August till the middle 
of September. The moon passes the sun on August 8th and 
September 6th of that year, which are, therefore, the dates of 
new moon. At the first date, the moon passes so far to the 
north that, as seen from the centre of the earth, there is no 
eclipse at all; but in the northern part of Asia the moon 
would be seen to cut off a small portion of the sun. 

While the moon is performing another circuit, the sun has 
moved so far past the node, that the moon passes south of it, 
and there is only a small eclipse, and that is visible only 
around the region of Cape Horn. Thus, there are two solar 
eclipses while the sun is passing this node in 1877, but both 
are very small. Indeed, every time the sun crosses a node, 
the moon is sure to cross his path, either before he reaches 
the node, or before he gets far enough from it to be out of 
the way. As he crosses both nodes in the course of the year, 
there must be at least two solar eclipses every year to some 
points of the earth's surface. 

The cause of lunar eclipses might not have been so easy to 
guess as was that of solar ones; but a great number could 



ECLIPSES OF THE SUN AND MOON. 2o 

hot have been observed, and their times of occurrence record- 
ed, without its being noticed that they always occurred at full 
moon, when the earth was opposite the sun. The idea that 
the earth cast a shadow, and that the moon passed into it, 
could then hardly fail to suggest itself ; and we find, accord- 
ingly, that the earliest observers of the heavens were perfectly 
acquainted with the cause of lunar eclipses. 

The reason why eclipses of the moon only occur occasion- 
ally is of the same general nature with that of the rare occur- 
rence of solar eclipses. The centre of the earth's shadow is 
always, like the sun, in the ecliptic ; and unless the moon hap- 
pens to be very near the ecliptic, and therefore very near one 
of her nodes at the time of full moon, she will fail to strike 
the shadow, passing above or below it. Owing to the great 
magnitude of the sun, the earth's shadow is, at the distance of 
the moon, much smaller than the earth itself. The result of 
this is, that the moon must be decidedly nearer her node to 
produce a lunar than to produce a solar eclipse. Sometimes 
a whole year passes without there being any eclipse of the 
moon. 

The nature of an eclipse will vary with the positions and 
apparent magnitudes of the sun and moon. Let us suppose, 
first, that, in a solar eclipse, the centre of the moon happens 
to pass exactly over the centre of the sun. Then, it is clear 
that if the apparent angular diameter of the moon exceed that 
of the sun, the latter will be entirely hidden from view. This 
is called a total eclipse of the sun. It is evident that such an 
eclipse can occur only w r hen the observer is near the line join- 
ing the centres of the sun and moon. If, under the same cir- 
cumstances, the apparent magnitude of the moon is less than 
that of the sun, it is evident that the whole of the latter cannot 
be covered, but a ring of light around his edge will still be visi- 
ble. This is called an annular eclipse. If the moon does not 
pass centrally over the sun, then it can cover only a portion of 
the latter on one side or the other, and the eclipse is said to be 
partial. So with the moon : if the latter is only partially im- 
mersed in the earth's shadow, the eclipse of the moon is called 



26 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

partial; if she is totally immersed in it, so that no direct sun- 
light can reach her, the eclipse is said to be total. An an- 





Fig. 6.— Annular eclipse of the sun. 



Fig. 7.— Partial eclipse of the sun. 



nular eclipse of the moon is impossible, because the earth's 
shadow always exceeds the diameter of the moon in breadth. 

Some points respecting eclipses will be seen more clearly 
by reference to the accompanying figures, in which 8 repre- 
sents the sun, E the earth, and M the moon. Kef erring to the 
first figure, it will be seen that an observer at either of the 
points marked O, or indeed anywhere outside the shaded por- 
tions, will see the whole of the sun, so that to him there will 
be no eclipse at all. Within the lightly shaded regions, marked 
PP, the sun will be partially eclipsed, and more so as the ob- 
server is near the centre. This region is called the penumbra. 




Fig. 8.— Eclipse of the sun, the shadow of the moon falling on the earth. 

Within the darkest parts between the two letters P is a region 
where the sun is totally hidden by the moon. This is the 
shadow, and its form is that of a cone, with its base on the 
moon, and its point extending towards the earth. Now, it 
happens that the diameters of the sun and -moon are very 
nearly proportional to their respective mean distances, so that 
the point of this shadow almost exactly reaches the surface of 
the earth. Indeed, so near is the adjustment, that the dark 
shadow sometimes reaches the earth, and sometimes does not, 



ECLIPSES OF THE SUN AXD MOON. 



owing to the small changes in the distance of the sun and 
moon. When the shadow reaches the earth, it is comparative- 
ly very narrow, owing to its being so near its sharp point; but 
if an observer can station himself within it, he will see a total 
eclipse of the sun during the short time the shadow is passing 
over him. If the reader will study the figure, he will see why 
a total eclipse of the sun is so rare at any one place on the 
earth. The shadow, when it reaches the earth, is so near down 
to a point that its diameter is not generally more than a hun- 
dred miles; consequently, each total eclipse is visible only 
along a belt which may not average more than a hundred 
miles across. 

In most eclipses, the shadow comes to a point before it 
reaches the earth ; in this case, the apparent angular diameter 
of the moon is less than that of the sun, and there can be do 
total eclipse. But if an observer places himself in a line with 
the centre of the shadow, he will see an annular eclipse, the 
sun showing itself on all sides of the moon. 

The next figure shows us the form of the earth's shadow. 




Fig. 9.— Eclipse of the moon, the latter being in the shadow of the earth. 

The earth being much larger than the moon, its shadow ex- 
tends far beyond it; and where it reaches the moon, it is al- 
ways so much larger than the latter that she may be wholly 
immersed in it, as shown in the figure. Now, suppose the 
moon, in her course round the earth, to pass centrally through 
the shadow, and not above or below it, as she commonly does ; 
then, when she entered the shaded region, marked JP, which 
is called the penumbra, an observer on her surface would see 
a partial eclipse of the sun caused by the intervention of the 



28 SYSTEM OF THE WOELD HISTORICALLY DEVELOPED. 

earth. The time when this begins is given in the almanacs, 
being expressed by the words, " Moon enters penumbra." 
Some of the sunlight is then cut off from the moon, so that 
the latter is not so bright as usual; but the eye does not 
notice any loss of light until the moon almost reaches the 
dark shadow. As she enters the shadow, a portion of her sur- 
face seems to be cut off and to disappear entirely, and her vis- 
ible portion continually grows smaller, until, in case of a total 
eclipse, her whole disk is immersed in the shadow. When this 
occurs, it is found that she is not entirely invisible, but still 
faintly shines with a lurid copper-colored light. This light is 
refracted into the shadow by the earth's atmosphere, and its 
amount may be greater or less, according to the quantity of 
clouds and vapor in the atmosphere around that belt of the 
earth which the sunlight must graze in order to reach the moon. 

In about half of the lunar eclipses, the moon passes so far 
above or below the centre of the shadow that part of her body 
is in it, and part outside, at the time of greatest eclipse. This 
is called a partial eclipse of the moon. The magnitude of a 
partial eclipse, whether of the sun or moon, was measured by 
the older astronomers in dibits. The diameter of the solar or 
lunar disk was divided into twelve equal parts, called digits ; 
and the magnitude of the eclipse was said to be equal to the 
number of digits cut off by the shadow of the earth in case of 
a lunar eclipse, or by the moon in case of a solar eclipse. The 
most ancient astronomers were in the habit of measuring the 
digits by surface : when the moon was said to be eclipsed four 
digits, it meant that one -third of her surface, and not one- 
third her diameter, was eclipsed. 

The duration of an eclipse varies between very wide limits, 
according to whether it is nearly central or the contrary. The 
duration of a solar eclipse depends upon the time required for 
the moon to pass over the distance from where she first comes 
into apparent contact with the sun's disk, until she separates 
from it again ; and this, in the case of eclipses w T hich are pret- 
ty large, may range between two and three hours. In a total 
*eclipse, however, the apparent disk of the moon exceeds that 






ECLIPSES OF THE SUN AXD MOON. 29 

of the sun by so small an amount, that it takes her but a short 
time to pass far enough to uncover some part of the sun's 
disk; the time is rarely more than live or six minutes, and 
sometimes only a few seconds. A total eclipse of tlie moon 
may, however, last nearly two hours, and the partial eclipses 
on each side of the total one may extend the whole duration 
of the eclipse to three or four hours. 

Total eclipses of the sun afford very rare and highly prized 
opportunities for studying the operations going on around that 
luminary. Of these we shall speak in a subsequent chapter. 

Returning, now, to the apparent motions of the sun and 
moon around the celestial sphere, we see that since the moon's 
orbit has two opposite nodes in which it crosses the ecliptic, 
and the sun passes through the entire course of the ecliptic in 
the course of the year, it follows that there are two periods in 
the course of a year during which the sun is near a node, and 
eclipses may occur. Roughly speaking, these periods are each 
about a month in duration, and we may call them seasons of 
eclipses. For instance, it will be seen on Map V. that the 
sun passes one node of the moon's orbit towards the end of 
February, 1877. A season of eclipses for that year is there- 
fore February and the first half of March. Actually, there is 
a total eclipse of the moon on February 27th, and a very small 
eclipse of the sun on March 14th, of that year, visible only in 
Northern Asia.* From this time, the sun is so far from the 
node that there can be no eclipses until he approaches the 
other node in August. Then we have the two eclipses of the 
sun already mentioned, and, between them, a total eclipse of 
the moon on August 23d. Thus, in the year 1S77, the first 
season of eclipses is in February and March, and the second 
in August and September. 

We have said that the length of each eclipse season is about 
a month. To speak with greater accuracy, the average season 
for eclipses of the sun extends 18 days before and after the 

* There is an extraordinary coincidence between this eclipse and that of Au- 
gust 8th of the same year, both being visible from nearly the same region in Cen- 
tral Siberia. 



30 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

sun's passage through the node, while that for lunar eclipses 
extends 11 J- days on each side of the node. The total season 
is, therefore, 36 days for solar, and 23 days for lunar eclipses. 

Owing to the constant motion of the moon's node already 
described, the season of eclipses will not be the same from 
year to year, but will occur, on the average, about 20 days 
earlier each year. We have seen that the sun passed the de- 
scending node of the moon marked on Map III. on August 
24th, 1877; but during the year following the node will have 
moved so far to the west that the sun will again reach it on 
August 5th, 1878. The effect of this constant shifting of the 
nodes and seasons of eclipses is that in 1887 the August sea- 
son will be shifted back to February, and the February season 
to August. The reader who wishes to find the middle of the 
eclipse seasons for twenty or thirty years can do so by starting 
from March 1st and August 24th, 1877, and subtracting 19f 
days for each subsequent year. 

There is a relation between the motions of the sun and 
moon which materially assisted the early astronomers in the 
prediction of eclipses. We have said that the moon makes 
one revolution among the stars in about 27-g- days. Since the 
node of the orbit is constantly moving back to meet the moon, 
as it were, she will return to her node in a little less than this 
period — namely, as shown by modern observations, in a mean 
interval of 27.21222 da}'S. The sun, after passing any node 
of the orbit, will reach the same node again in 346.6201 days. 
The relation between these numbers is this : 242 returns of 
the moon to a node take very nearly the same time with 19 
returns of the sun, the intervals being 

242 returns of the moon to her node 6585.357 days; 

19 " " sun to moon's node 6585.780 " 

Consequently, if at any time the sun and moon should start 
out together from a node, they would, at the end of 6585 
days, or 18 years and 11 days, be again found together very 
near the same node. During the interval, there would have 
been 223 new and full moons, but none so near the node as 



ECLIPSES OF THE SUN AND MOON 31 

this. The. exact time required for 223 lunations is 6585.3212 
days; so that, in the case supposed, the 223d conjunction of 
the sun and moon would happen a little before they readied 
the node, their distance from it being, by calculation, a little 
less than one of their diameters, or, more exactly, 28'. If, 
instead of being exactly at the node, they are any given dis- 
tance from it, say 3° east or west, then, in the same period, 
they will be again together within half a degree of the same 
distance from the node. 

The period just found was called the Saros, and may be ap- 
plied in this way : Let us note the exact time of the middle 
of any eclipse, either of the moon or of the sun ; then let us 
count forwards 6585 days, 7 hours, 42 minutes, and we shall 
find another eclipse of very nearly the same kind. Reduced 
to years, the interval will be 18 years and 10 or 11 days, ac- 
cording to whether the 29th of February has intervened four 
or five times during the interval. This being true of every 
eclipse, if we record all the eclipses which occur during a 
period of 18 years, we shall find the same series after 10 or 
11 days to begin over again ; but the new series will not gen- 
erally be visible at the same places with the old ones, or, at 
least, will not occur at the same time of day, since the mid- 
dle will be nearly eight hours later. Not till the end of three 
periods will they recur near the same meridian ; and then, 
owing to the period not being exact, the eclipse will not be 
precisely of the same magnitude, and, indeed, may fail entire- 
ly. Every successive recurrence of an eclipse at the end of 
the period being 2S' farther back relatively to the node, the 
conjunction must, in process of time, be so far back from the 
node as not to produce an eclipse at all. During nearly every 
period it will be found that some eclipse fails, and that some 
new one enters in. A new eclipse of the moon thus entering 
will be a very small one indeed. At every successive recur- 
rence of its period it will be larger, until, about its thirteenth 
recurrence, it will be total. It will be total for about twenty- 
two or twenty-three recurrences, when it will become partial 
once more, but on the opposite side of the moon from that on 

4 



32 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

which it was first seen. There will then be about thirteen par- 
tial eclipses, each smaller than the last, until they fail entirely. 
The whole interval of time over which the recurrence of a 
lunar eclipse thus extends will be about 48 periods, or 865^ 
years. The solar eclipses, occurring farther from the node, 
will last yet longer, namely, from 65 to 70 periods, or over 
1200 years. 

As a recent example of the Saros, we may cite some total 
eclipses of the sun well known in recent times ; for instance, 

1842, July 8th, l h 8 a.m., total eclipse, observed in Europe; 

1860, July 18th, 9 h a.m., total eclipse America and Spain ; 

1878, July 29th, 4 h 2 p.m., one visible in Colorado and on the Pacific Coast. 

A yet more remarkable series of total eclipses of the sun 
occurs in the years 1850, 1868, 1886, etc., the dates being — 

1850, August 7th, 4 h 4 p.m., in the Pacific Ocean ; 

1868, August 17th, 12 h p.m., in India ; 

1886, August 29th, 8 h a.m., in the Central Atlantic Ocean and Southern Africa; 

1904, September 9th, noon, in South America. 

This series is remarkable for the long duration of totality, 
amounting to some six minutes. 

It must be understood that the various numbers we have 
given in this section are not accurate for all cases, because the 
motions both of the sun and moon are subject to certain small 
irregularities which may alter the times of eclipses by an hour 
or more. We have given only mean values, which are, how- 
ever, always quite near the truth. 

§ 7. The Ptolemaic System. 

There is still extant a work which for fourteen centuries 
was a sort of astronomical Bible, from which nothing was 
taken, and to which nothing material in principle was added. 
This is the "Almagest" of Ptolemy, composed about the mid- 
dle of the second century of our era. Nearly all we know of 
the ancient astronomy as a science is derived from it. Frag- 
ments of other ancient authors have come down to us, and 
most of the ancient writers make occasional allusions to astro- 
nomical phenomena or theories, from which various ideas re- 






THE PTOLEMAIC SYSTEM. 33 

speeting the ancient astronomy have been gleaned; bnt the 
work of Ptolemy is the only complete compendium which we 
possess. Although his system is in several important points 
erroneous, it yet represents the salient features of the apparent 
motions of the heavenly bodies with entire accuracy. Defec- 
tive as it is when measured by our standard, it is a marvel of 
ingenuity and research when measured by the standard of the 
times. 

The immediate object of the present chapter is to explain 
the apparent movements of the planets, which can he most 
easily done on the Ptolemaic system. But, on account of it> 
historic interest, we shall begin with a brief sketch of the 
propositions on which the system rests, giving also Ptolemy's 
method of proving them. His fundamental doctrines are that 
the heavens are spherical in form, and all the heavenly mo- 
tions spherical or in circles; that the earth is alsu spherical, 
and situated in the centre of the heavens, or celestial sphere, 
where it remains quiescent, and that it is in magnitude only a 
point when compared with the sphere of the stars. We shall 
give Ptolemy's views of these propositions, and his attempts 
to prove them, in their regular order. 

1st. The Heavenly Bodies move in Circles. — Here Ptole- 
my refers principally to the diurnal motion, whereby every 
heavenly body is apparently carried around the earth, or, rath- 
er, around the pole of the heavens, in a circle every day. But 
all the ancient and mediaeval astronomers down to the time 
of Kepler had a notion that, the circle being the most perfect 
plane figure, all the celestial motions must take place in cir- 
cles; and as it was found that the motions were never uni- 
form, they supposed these circles not to be centred on the 
earth. Where a single circle did not suffice to account for 
the motion, they introduced a combination of circular motions 
in a manner to be described presently. 

2d. The Earth is a Sphere. — That the earth is rounded 
from east to west Ptolemy proves by the fact that the sun, 
moon, and stars do not rise and set at the same moment to all 
the inhabitants of the earth. The times at which eclipses of 



34 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

the moon are seen in different countries being compared, it is 
found that the farther the observer is west, the earlier is the 
hour after simset. As the time is really the same everywhere, 
this shows that the sun sets later the farther we go to the west. 
Again, if the earth were not rounded from north to south, a 
star passing the meridian in the north or south horizon would 
always pass in the horizon, however far to the north or south 
the observer might travel. But it is found that when an ob- 
server travels towards the south, the stars in the north ap- 
proach the horizon, and the circles of their diurnal motion cut 
below it, while new stars rise into view above the south hori- 
zon. This shows that the horizon itself changes its direction 
as the observer moves. Finally, from whatever direction we 
approach elevated objects from the sea, we see that their bases 
are first hidden from view by the curvature of the water, and 
gradually rise into view as we approach them. 

3d. The Earth is in the Centre of the Celestial Sphere. — 
If the earth were displaced from the centre, there would be 
various irregularities in the apparent daily motion of the ce- 
lestial sphere, the stars appearing to move faster on the side 
towards which the earth was situated. If it were displaced 
towards the east, we should be nearer the heavenly bodies 
when they are rising than when they are setting, and they 
would appear to move more rapidly in the east than in the 
west. The forenoons would therefore be shorter than the af- 
ternoons. Towards whatever side of the turning sphere it 
might be moved, the heavenly bodies would seem to move 
more rapidly on that side than on the other. Eo such irreg- 
ularity being seen, but the diurnal motion taking place with 
perfect uniformity, the earth must be in the centre of mo- 
tion. 

4th. The Earth has no Motion of Translation — Because 
if it had it would move away from the centre towards one 
side of the celestial sphere, and the diurnal revolution of the 
stars w r ould cease to be uniform in all its parts. But the uni- 
formity of motion just described being seen from year to year, 
the earth must preserve its position in the centre of the sphere. 



THE PTOLEMAIC SYSTEM. 35 

It will be interesting to analyze these propositions of Ptole- 
my, to see what is true and what is false. The first proposi- 
tion — that the heavenly bodies move in circles, or, as it is 
more literally expressed, that the heavens move spherically — 
is quite true, so far as the apparent diurnal motion is con- 
cerned. What Ptolemy did not know was that this motion la 
only apparent, arising from a rotation of the earth itself on its 
axis. The second proposition is perfectly correct, and Ptole- 
my's proofs that the earth is round are those still found in our 
school-books at the end of seventeen hundred years. Most 
curious, however, is the mixture of truth and falsehood in the 
third and fourth propositions, that the earth remains quies- 
cent. We cannot denounce it as unqualifiedly false, because, 
in a certain sense, and indeed in the only sense in which there 
is any celestial sphere, the earth may be said to remain in the 
centre of the sphere. What Ptolemy did not see is that this 
sphere is only an ideal one, which the spectator carries with 
him wherever he goes. His demonstration that the centre of 
revolution of the sphere is in the earth is, in a certain sense, 
correct ; but what he really proves is that the earth revolves 
on its own axis. He did not see that if the earth could carry 
the axis of revolution with it, his demonstration of the quies- 
cence of the earth would fall, to the ground. 

Considerable insiffht into Ptolemv's views is gained bv his 
answers to two objections against his system. The first is the 
vulgar and natural one, that it is paradoxical to suppose that 
a body like the earth could remain supported on nothing, and 
still be at rest. These objectors, he says, reason from what 
they see happen to small bodies around them, and not from 
what is proper to the universe at large. There is neither up 
nor down in the celestial spaces, for we cannot conceive of it 
in a sphere. What we call down is simply the direction of 
our feet towards the centre of the earth, the direction in 
which heavy bodies tend to fall. The earth itself is but a 
point in comparison with the celestial spaces, and is kept fixed 
by the forces exerted upon it on all sides by the universe, 
which is infinitely larger than it, and similar in all its parts. 



36 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

This idea is as near an approach to that of universal gravita- 
tion as the science of the times would admit of. 

He then says there are others who, admitting this reason- 
ing, pretend that nothing hinders us from supposing that the 
heavens are immovable, and that the earth itself turns round 
its own axis once a day from west to east. It is certainly 
singular that one who had risen so far above the illusions of 
sense as to demonstrate to the world that the earth was round ; 
that up and down were only relative ; and that heavy bodies 
fell towards a centre, and not in some unchangeable direction, 
should not have seen the correctness of this view. 

To refute the doctrine of the earth's rotation, he proceeds 
in a way the opposite -of that w T hich he took to refute those 
who thought the earth could not rest on nothing. He said of 
the latter that they regarded solely what was around them on 
the earth, and did not consider what was proper to the uni- 
verse at large. To those who maintained the earth's rotation, 
he says, if we consider only the movements of the stars, there 
is nothing to oppose their doctrine, which he admits has the 
merit of simplicity; but in view of what passes around us and 
in the air, their doctrine is ridiculous. He then enters into a 
disquisition on the relative motion of light and heavy bodies, 
which is extremely obscure ; but his conclusion is that' if the 
earth really rotated with the enormous velocity necessary to 
carry it round in a day, the air would be left behind. If they 
say that the earth carries round the air with it, he replies that 
this could not be true of bodies floating in the air ; and hence 
concludes that the doctrine of the earth's rotation is not tena- 
ble. It is clear, from this argument, that if Ptolemy and his 
contemporaries had devoted to experimental physics half the 
careful observation, research, and reasoning which we find in 
their astronomical studies, they could not have failed to estab- 
lish the doctrine of the earth's rotation. 

In the Ptolemaic system, all the celestial motions are repre- 
sented by a series of circular motions. We have already ex- 
plained the motions of the sun and moon among the stars, the 
first describing a complete circuit of the heavens from west to 



TEE PTOLEMAIC SYSTEM. 3< 

east in a year, and the second a similar circuit in a month. 
Though not entirely uniform, these movements are always for- 
ward. But it is not so with the five planets — Mercury, Ve- 
nus, Mars, Jupiter, and Saturn. These move sometimes to the 
east and sometimes to the west, and are sometimes stationary. - 
On the whole, however, the easterly movements predominate ; 
and the planets really oscillate around a certain mean point 
itself in regular motion towards the east. Let us take, for in- 
stance, the planet Jupiter. Suppose a certain fictitious Jupi- 
ter performing a circuit of the heavens among the stare every 
twelve years with a regular easterly motion, just as the son 
performs such a circuit every year; then the real Jupiter will 
be found to oscillate, like a pendulum, on each side of the fic- 
titious planet, but never swinging more than 12" from it. The 
time of each double oscillation is about thirteen months — that 
is, if on January 1st we find it passing the fictitious planet 
towards the west, it will continue its westerly swing about 
three months, when it will gradually stop, and return with a 
somewhat slower motion to the fictitious planet again, passing 
to the east of it the middle of July. The easterly swinir will 
continue till about the end of October, when it will return 
towards the west. The westerly or backward motion is called 
retrograde, and the easterly motion direct. Between the two 
is a point at which the planet appears stationary once more. 
The westerly motions are called retrograde because they are 
in the opposite direction both to the motion of the sun among 
the stars, and to the average direction in which all the planets 
move. It was seen by Hipparchus, who lived three centuries 
before Ptolemy, that this oscillating motion could be repre- 
sented by supposing the real Jupiter to describe a circular or- 
bit around the fictitious Jupiter once in a year. This orbit is 
called the epicycle, and thus we have the celebrated epicyclic 
theory of the planetary motions laid down in' the "Almagest." 
The movement of the planet on this theory can be seen by 

* It may not be amiss to remind the reader once more that we here leave the 
diurnal motion of the stars entirely out of sight, and consider only the motions of 
the planets relative to the stars. 



38 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 



Fig. 



10. E is the earth, around which the fictitious Jupiter 
moves in the dotted circle, 1, 2, 3, 4, etc. To form the epicycle 
in which the real planet moves, we must suppose an arm to be 
constantly turning round the fictitious planet once a year, on 
the end of which Jupiter is carried. This arm will then be in 
the successive positions, 1 1', 2 2', 3 3', etc., represented by the 
light dotted lines. Drawing a line through the successive po- 
sitions 1', 2', 3', etc., of the real Jupiter, we shall have a series 
of loops representing its apparent orbit. 




Fig. 10.— Showing the apparent orbit of a planet, regarding the earth as at rest. 

It will be seen that although it requires only a year for the 
arm carrying the real Jupiter to perform a complete revolu- 
tion and return to its primitive direction, it requires about 
thirteen months to form a complete loop, because, owing to 
the motion of the fictitious planet in its orbit, the arm must 
move more than a complete revolution to finish the loop. For 
instance, referring again to Fig. 10, comparing the positions 
1 V and 8 8', it will be seen that the arm, being in the same 
direction, has performed a complete revolution ; but, owing to 
the curvature of the orbit, it does not reach the middle of the 
second loop until it attains the position 9 9'. 



TEE PTOLEMAIC SYSTEM. 



30 



The planets of which the radius of the epicycle makes an 
animal revolution in this way are Mars. Jupiter, and Saturn. 
The complete apparent orbits of the last two planets arc shown 
in the next figure, taken from Arago. By the radius of the 
epicycle we mean the imaginary revolving arm which, turn- 
ing round the fictitious planet, carries the real planet at its 




Fig. 11.— Apparent orbits of Jupiter and Saturn, 170S-1737, after Cassini. 

end. The law of revolution of this arm is, that whenever the 
planet is opposite the sun, the arm points towards the earth, 
as in the positions 1 1', 9 9', in which cases the sun will be on 
the side of the earth opposite the planet ; while, whenever the 
planet is in conjunction with the sun, the arm points from the 
earth. This fact was well known to the ancient astronomers, 
and their calculations of the motions of the planets were all 



40 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

founded upon it; but they do not seem to have noticed the 
very important corollary from it, that the direction of the 
radius of the epicycle of Mars, Jupiter, and Saturn is always 
the same with that of the sun from the earth. Had they 
done so, they could hardly have failed to see that the epicycles 
could be abolished entirely by supposing that it was the earth 
which moved round the sun, and not the sun round the earth. 
The peculiarity of the planets Mercury and Yenus is that 
the fictitious centres around which they oscillate are always in 
the direction of the sun, or, as we now know, the sun himself 
is the centre of their motions. They are never seen more than 
a limited distance from that luminary, Yenus oscillating about 
45° on each side of the sun, and Mercury from 16° to 29°. It 
is said that the ancient Egyptians really did make the sun the 
centre of the motion of these two planets ; and it is difficult to 
see how any one could have failed to do so after learning the 
laws of their oscillation. Yet Ptolemy rejected this system, 
placing their orbits between the earth and sun without assign- 
ing any good reason for the course. 

The arrangement of the planets on the Ptolemaic system is 
shown in Fig. 12. The nearest planet is the moon, of which 
the ancient astronomers actually succeeded in roughly meas- 
uring the distance. The remaining planets are arranged in 
the same order with their real distance from the sun, except 
that the latter takes the place assigned to the earth in the 
modern system. Thus we have the following order : 

The Moon, 

Mercury, 

Yenus, 

The Sun, 

Mars, 

Jupiter, 

Saturn. 
Outside of Saturn was the sphere of the fixed stars. 

This order of the planets must have been a matter of opin- 
ion rather than of demonstration, it being correctly judged 
by the ancient astronomers that those which seemed to move 



THE PTOLEMAIC SYSTEM. 

Saturn 



41 




Fig. 12.— Arrangement of the seven planets in the Ptolemaic system. The orbit=. M 
marked, are those of the fictitious planets, the real planets being supposed to describe 
a series of loops. 

more slowly were the more distant. This system made it 
quite certain that the moon was the nearest planet, and Mars, 
Jupiter, and Saturn, in their order, the most distant ones. But 
the relative positions of the Sun, Mercury, and Venus were 
more in doubt, since they all performed a revolution round 
the celestial sphere in a year. So, while Ptolemy, as we have 
just said, placed Mercury and Venus between the earth and 
the sun, Plato placed them beyond the sun, the order being, 
Moon, Sun, Mercury, Venus, Mars, Jupiter, Saturn. 

Hipparchus and Ptolemy made a series of investigations re- 
specting the times of revolution of the planets, and the inequal- 
ities of their motions, of which it is worth while to give a brief 



42 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 



summary. The former was no doubt an abler astronomer than 
Ptolemy ; but as he was, so far as we know, the first accurate 
observer of the celestial motions, he could not make a suf- 
ficiently long series of observations to determine all the peri- 
ods of the planets. Ptolemy had the advantage of being able 
to combine his own observations with those of Hipparchus, 
three centuries earlier. 

Imperfect though their means of observation were, these 
observers found that the easterly movements of the planets 
among the stars were none of them uniform. This held true 
not only of the sun and moon, but of the fictitious planets 

already described. Hence they 
invented the eccentric, and sup- 
posed the motions to be really cir- 
cular and uniform, but in circles 
not centred in the earth. In Fig. 
13, let E be the earth, and C the 
centre around which the planet 
really revolves. Then, when the 
planet is passing the point P, 
which is nearest the earth, its an- 
gular motion would seem more 
rapid than the average, because 
in general the angular velocity 
of a moving body is greater the 
nearer the observer is to it, while 
when passing A it will seem to be 
more slow than the average. The angular velocity being 
always greatest in one point of the orbit, and least in a point 
directly opposite, changing regularly from the maximum to 
the minimum, the general features of the movement are cor- 
rectly represented by the eccentric. By comparing the angu- 
lar velocities in different points of the orbit, Hipparchus and 
Ptolemy were able to determine the supposed distance of the 
earth from the centre, or rather the proportion of this distance 
to the distance of the planet. The distance thus determined 
is double its true amount. The point P is called the Perigee, 




Fig. 13. — The eccentric. Shows how 
the ancients represented the unequal 
apparent velocities of the planets 
when their real motion was supposed 
uniform, by placing the earth away 
from the centre of motion, at E. 



THE PTOLEMAIC SYSTEM. 43 

and A the Apogee. The distance CE from the earth to the 
centre of motion is the eccentricity. As there was no way of 
determining the absolute dimensions of the orbit, it was neces- 
sary to take the ratio of CE to the radius of the orbit CP or 
CEiov the eccentricity.* 

In determining the motions of the moon, Hipparchus and 
Ptolemy depended almost entirely on observations of lunar 
eclipses. The first of these, it is said, was observed at Babylon 
in the first year of Mardocempad, between the 2 ( Jth and 30th 
days of the Egyptian month Thoth. It commenced a little 
more than an hour after the moon rose, and was total. The 
date, in our reckoning, was b.c. 720, March 19th. The series 
of eclipses extended from this date to that of Ptolemy him- 
self, who lived between eight and nine centuries later. If the 
observations of these eclipses had been a little more precise, 
they would still be of great value to us in fixing the mean 
motion of the moon. As it is, we can now calculate the cir- 
cumstances of an ancient eclipse from our modern tables of 
the sun and moon almost as accurately as any of the ancient 
astronomers could observe it. 

Notwithstanding the extremely imperfect character of the 
observations, both Hipparchus and Ptolemy made discoveries 
respecting the peculiarities of the moon's motions which show 
a most surprising depth of research. By comparing the inter- 
vals between eclipses, they found that her motion was not uni- 
form, but that, like the sun, she moved faster in some parts of 
her orbit than in others. To account for this, they supposed 
her orbit eccentric, like that of the sun ; that is, the earth, in- 
stead of being in the centre of the circular orbit of the moon, 
was supposed to be displaced by about a tenth part the whole 
distance of that body. So far the orbit of the moon was like 
that of the sun and the fictitious planets, except that its eccen- 
tricity was greater. But a long series of observations showed 

* Compared with the modern theory of the elliptic motion, approximately treat- 
ed, the distance CE is double the eccentricity of the ellipse. One-half the appar- 
ent inequality is really caused by the orbit being at various distances from the 
earth or sun, but the other half is real. 



44 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 

that the perigee and apogee did not, as in the case of the son 
and planets, remain in the same points of the orbit, but moved 
forwards at such a rate as to carry them round the heavens in 
nine years ; that is, supposing Fig. 13 to represent the orbit of 
the moon, the centre of the circle C revolved round the earth 
jn nine years, and the orbit changed its position accordingly. 

It was also found by Ptolemy, by measuring the apparent 
angle between the moon and sun in various points of the 
orbit of the former, that there was yet another inequality in 
her motion. This has received the name of the evection. In 
consequence of this inequality, the moon oscillates more than 
a degree on each side of her position as calculated from the 
eccentric, in a period not differing much from her revolution 
round the earth. To represent this motion, Ptolemy had to 
introduce a small additional epicycle, as in the case of the 
planets, only the radius was so small that there was no looping 
of the orbit. In consequence, his theory of the moon's motion 
was quite complicated; yet he managed to represent this mo- 
tion, within the limits of the errors of his observations, by a 
combination of circular motions, and thus saved the favorite 
theory of the times, that all the celestial motions were circular 
and uniform. 

§ 8. The Calendar. 

One of the earliest purposes of the study of the celestial 
motions was that of finding a convenient measurement of 
time. This application of astronomy, being of great antiquity, 
having been transmitted to us without any fundamental altera- 
tion, and depending on the apparent motions of the sun and 
moon, which we have studied in this chapter, is naturally con- 
sidered in connection with the ancient astronomy. 

The astronomical divisions of time are the day, the month, 
and the year. The week is not such a division, because it does 
not correspond to any astronomical cycle, although, as we shall 
presently see, a certain astronomical signification was said to 
have been given to it by the ancient astrologers. Of these 
divisions the day is the most w T ell-marked and striking through- 



THE CALENDAR. 45 

out the habitable portion of the globe. Had a people lived at 
or near the poles, it would have been less striking than the year. 
But wherever man existed, there was a regular alternation of 
day and night, with a corresponding alternation in his physical 
condition, both occurring with such regularity and uniformity 
as to furnish in all ages the most definite unit of time. For 
merely chronological purposes the day would have been the 
only unit of time theoretically necessary ; for if mankind had 
begun at some early age to number every day by counting 
from 1 forwards without limit, and had every historical event 
been recorded in connection with the number of the day on 
which it happened, there would have been far less uncertain- 
ty abaut dates than now exists. But keeping count of such 
large numbers as would have accumulated in the lapse of cen- 
turies would have been very inconvenient, and a simple count 
of time by days has never been used for the purposes of civil 
life through any greater period than a single month. 

Next to the day, the most definite and striking division of 
time is the year. The natural year is that measured by the 
return of the seasons. All the operations of agriculture are 
so intimately dependent on this recurrence, that man must 
have begun to make use of it for measuring time long before 
he had fully studied the astronomical cause on which it de- 
pends. The years in the lifetime of any one generation not 
being too numerous to be easily reckoned, the year was found 
to answer every purpose of measuring long intervals of time. 

The number of days in the year is, however, too great to 
be conveniently kept count of; an intermediate measure was 
therefore necessary. This was suggested by the motion and 
phases of the moon. The " new moon " being seen to emerge 
from the sun's rays at intervals of about 30 days, a measure 
of very convenient length was found, to which a permanent 
interest was attached by the religious rites connected with the 
reappearance of the moon. 

The week is a division of time entirely disconnected with 
the month and year, the employment of which dates from the 
Mosaic dispensation. The old astrologers divided the seven 



46 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 

days of the week among the seven planets, not in the order of 
their distance from the sun, but in one shown by the follow- 
ing figure. If we go round the circle in the direction of the 
hands of a watch, we shall find the names of the seven plan- 
ets of the ancient astronomy, in the order of their supposed 
distances ;* while, if we follow the lines drawn in the circle 
from side to side, we shall have the days of the week in their 
order. 



<j\i.ats 




-AW* if 



^SSS» 



Fig. 14.— Showing the astrological division of the seven planets among the days of the 

week. 

If the lunar month had been an exact number of days, say 
30, and the year an exact number of months, as 12, there 
would have been no difficulty in the use of these cycles for 
the measurement of time. But the former is several hours 
less than 30 days, while the latter is nearly 12-| lunar months. 
In the attempt to combine these measures, the ancient calen- 



* See pages 40, 41. 






THE CALENDAR. 47 

dars were thrown into a confusion which made them very per- 
plexing, and which we see to this day in the irregular lengths 
of our months. To* describe all the devices which we know to 
have been used for remedying these difficulties would be very 
tedious; we shall therefore confine ourselves to their general 
nature. 

The lunar month, or the mean interval between successive 
new moons, is very nearly 29J days. In counting months by 
the moon, it was therefore common to make their length 29 
and 30 days, alternately. But the period of 21H days is really 
about three-quarters of an hour too short. In the course of 
three years the count will therefore be a day in error, and it 
will be necessary to add a day to one of the months. When 
lunar months were used, the year, comprising 12 such months, 
would consist of only 354 days, and would there {ore be 11 
days too short. Nevertheless, such a year was used both by 
the Greeks and Bomans, and is still used by the Mahome- 
tans ; the Romans, however, in the calendar of Nnma, adding 
22 or 23 days to every alternate year by inserting the inter- 
calary month Mercedonius between the 23d and 24th of Feb- 
ruary. 

The irregularity and inconvenience of reckoning by lunar 
months caused them to be very generally abandoned, the only 
reason for their retention bein^ religious observances due at 
the time of new moon, which, among the Jews and other an- 
cient nations, were regarded as of the highest importance. Ac- 
cordingly, we find the E^vptians counting bv months of 30 
days each, and making every year consist of 12 such month? 
and five additional days, making 365 days in all. As the true 
length of the year was known to be about six hours greater 
than this, the equinox would occur six hours later every year, 
and a month later after the lapse of 120 years. After the lapse 
of 1460 years, according to the calculations of the time, each 
season would have made a complete course through the twelve 
months, and would then have returned once more at the same 
time of year as in the beginning. This was termed the Sothic 
Period; but the error of each year being estimated a little 

5 



4S SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

too great, as we now know, the true length of the period 
would have been about 1500 years. 

The confusion in the Greek year was partly remedied 
through the discovery by Meton of the cycle which has since 
borne his name. This cycle* consists of 19 solar years, during 
which the moon changes 235 times. The error of this cycle 
is very small, as may be seen from the following periods, com- 
puted from modern data : 

Days. Hours. Min. 

235 lunations require in the mean 6939 16 31 

19 true solar years (tropical) 6939 14 27 

19 Julian years of 365£ days 6939 18 

Hence, if we take 235 lunar months, and divide them up as 
nearly evenly as is convenient into 19 years, the mean length 
of these years will be near enough right for all the purposes 
of civil reckoning. The years of each cycle were numbered 
from 1 to 19, and the number of the year was called the Gold- 
en Number, from its having been ordered to be inscribed on 
the monuments in letters of gold. 

This is the only religious festival which, in Christian coun- 
tries, depends directly on the motion of the moon. The rule 
for determining Easter is that it is the Sunday following the 
first full moon which occurs on or after the 21st of March. 
The dates of the full moon correspond to the Metonic Cycle ; 
that is, after the lapse of 19 years they recur on or about the 
same day of the year. Consequently, if we make a list of the 
dates on which the Paschal full moon occurs, we shall find 
no two dates to be the same for nineteen successive years ; 
but the twentieth will occur on the same day with the first, 
or, at most, only one day different, and then the whole series 
will be repeated. Consequently, the Golden Number for the 
year shows, with sufficient exactness for ecclesiastical purposes, 
on what day, or how many days after the equinox, the Paschal 
full moon occurs. The church calculations of Easter Sunday 
are, however, founded upon very old tables of the moon, so 
that if we fixed it by the actual moon, we should often find 
the calendar feast a week in error. 



TEE CALEXDAE. 49 

The basis of the calendars now employed throughout Chris- 
tendom was laid by Julius Caesar. Previous to his time, the 
Roman calendar was in a state of great confusion, the nomi- 
nal length of the year depending very largely on the caprice 
of the ruler for the time being. It was, however, very well 
known that the real length of the solar year was about 365J 
days ; and, in order that the calendar year might have the same 
mean length, it was prescribed that the ordinary year should 
consist of 365 days, but that one day should be added to every 
fourth year. The lengths of the months, as we now have them, 
were finally arranged by the immediate successors of Caesar. 

The Julian calendar continued unaltered for about sixteen 
centuries; and if the true length of the tropical year had been 
365^ days, it would have been in use still. But, as we have 
seen, this period is about 11^ minutes longer than the solar 
year, a quantity which, repeated every year, amounts to an en- 
tire day in 128 years. Consequently, in the sixteenth century, 
the equinoxes occurred 11 or 12 days sooner than they should 
have occurred according to the calendar, or on the 10th in- 
stead of the 21st of March. To restore them to their original 
position in the year, or, more exactly, to their position at the 
time of the Council of Nicej was the object of the Gregorian 
reformation of the calendar, so called after Pope Gregory 
XIIL, by whom it was directed. The change consisted of 
two parts : 

1. The 5th of October, 1582, according to the Julian calen- 
dar, was called the 15th, the count being thus advanced 10 
days, and the equinoxes made once more to occur about March 
21st and September 21st. 

2. The closing year of each century, 1600, 1700, etc., in- 
stead of being each a leap-year, as in the Julian calendar, 
should be such only when the number of the century was di- 
visible by 4. While 1600, 2000, 2400, etc., were to "be leap- 
years, as before, 1700, 1S00, 1900, 2100, etc., were to be re- 
duced to 365 days each. 

This change in the calendar was soon adopted by the Catho- 
lic countries, and, more slowly, by Protestant ones — England, 



50 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

among the latter, holding out for more than a century, but 
finally entering into the change in 1752. In Russia it was 
never adopted at all, the Julian calendar being still continued 
in that country. Consequently, the Russian reckoning is now 
12 days behind ours, the 10 days' difference during the six- 
teenth and seventeenth centuries being increased by the days 
dropped from the years 1700 and 1800 in the new reckoning. 

The length of the mean Gregorian year is 365 d 5 h 49 m 12 s ; 
while that of the tropical year, according to the best astronom- 
ical determination, is 365 d 5 h 48 m 46 s . The former is, there- 
fore, still 26 seconds too long, an error which will not amount 
to an entire day for more than 3000 years. If there were 
any object in having the calendar and the astronomical years 
in exact coincidence, the Gregorian year would be accurate 
enough for all practical purposes during many centuries. In 
fact, however, it is difficult to show what practical object is to 
be attained by seeking for any such coincidence. It is im- 
portant that summer and winter, seed-time and harvest, shall 
occur at the same time of the year through several successive 
generations ; but it is not of the slightest importance that 
they should occur at the same time now that they did 5000 
years ago, nor would it cause any difficulty to our descendants 
of 5000 years hence if the equinox should occur in the middle 
of February, as would be the case should the Julian calendar 
have been continued. 

The change of calendar met with much popular opposition, 
and it may hereafter be conceded that in this instance the 
common sense of the people was more nearly right than the 
wisdom of the learned. An additional complication was in- 
troduced into the reckoning of time without any other real 
object than that of making Easter come at the right time. 
As the end of the century approaches, the question of making 
1900 a leap-year, as usual, will no doubt be discussed, and it is 
possible that some concerted action may be taken on the part of 
leading nations looking to a return to the old mode of reckoning. 



COPERMCW. 51 






CHAPTER II. 



ENLY BODIES. 



§ 1. Copernicus. 

In the first section of the preceding chapter we described 
the apparent diurnal motion of the heavens, whereby all the 
heavenly bodies appear to be carried round in circles, thus 
performing a revolution every day. Any observer of this mo- 
tion who should suppose the earth to be flat, and the direction 
we call downward everywhere the same, would necessarily re- 
gard it as real. A very little knowledge of geometry would, 
however, show him that the appearance might be accounted 
for by supposing the earth to revolve. The seemingly fatal 
objection against this view would be that, if such were the 
case, the surface of the earth could not remain level, and ev- 
ery thing would slide away from its position. But it was im- 
possible for men to navigate the ocean without perceiving the 
rotundity of its surface, and we have no record of a time when 
it was not known that the earth was round. We have seen 
that Ptolemy not only was acquainted with the true figure of 
the earth, but knew that in magnitude it was so much smaller 
than the celestial spaces, or sphere of the heavens, as to be only 
a point in comparison. He had, therefore, all the knowledge 
necessary to enable him to see that the moving body was much 
more likely to be the earth than to be the sphere of the heav- 
ens. Nevertheless, he rejected the theory on obscure physical 
grounds, as shown in the last chapter, the untenability of which 
would have been proved him by a few very simple physical ex- 
periments. And although it is known that the doctrine of the 
earth's motion was sustained by others in his age, notably by 
Timocharis, yet the weight of his authority was so great as 



52 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

not only to override all their arguments, but to carry his views 
through fourteen centuries of the intellectual history of man. 

The history of astronomy during these centuries offers hard- 
ly anything of interest to the general reader. There was no 
telescope to explore the heavens, and no genius arose of suffi- 
cient force to unravel the maze of their mechanism. It was 
mainly through the Arabs that any systematic knowledge of 
the science was preserved for the use of posterity. The as- 
tronomers of this people invented improved methods of ob- 
serving the positions of the heavenly bodies, and were thus 
able to make improved tables of their motions. They meas- 
ured the obliquity of the ecliptic, and calculated eclipses of 
the sun and moon with greater precision than the ancient 
Greeks could do. The predictions of the science thus gradu- 
ally increased in accuracy, but no positive step was taken in 
the direction of discovering the true nature of the apparent 
movements of the heavens. 

The honor of first proving to the world what the true theory 
of the celestial motions is belongs almost exclusively to Coper- 
nicus. It is true that we have some reason to believe that 
Pythagoras taught that the sun, and not the earth, was the 
centre of motion, and that he was, therefore, the first to solve 
the great problem. But he did not teach this doctrine public- 
ly, and the very vague statements of his private teachings on 
this point which have been handed down to us are so mixed 
up with the speculations which the Greek philosophers com- 
bined with their views of nature, that it is hard to say with 
precision whether Pythagoras had or had not fully seized the 
truth. It is certain that no modern would receive the credit 
of any discovery without giving more convincing proofs of the 
correctness of his views than we have any reason to suppose 
that Pythagoras gave to his disciples. 

The great merit of Copernicus, and the basis of his claim to 
the discovery in. question, is that he was not satisfied with a 
mere statement of his views, bnt devoted a large part of the 
labor of a life to their demonstration, and thus placed them in 
such a light as to render their ultimate acceptance inevitable. 



COPE EX IC US. 53 

Apart from all questions of the truth or falsity of his theory, 
the great work in which it was developed, "De Eevolutionibus 
Orbium Coelestium" would deservedly rank as the most im- 
portant compendium of astronomy which had appeared since 
Ptolemy. Few books have been more completely the labor of 
a lifetime than this. Copernicus was born at Thorn, in Prus- 
sia, in 1473, twenty years before the discovery of America, 
but studied at the University of Cracow. He became an ec- 
clesiastical dignitary, holding the rank of canon during a large 
portion of his life, and finding ample leisure in this position 
to pursue his favorite studies. He is said to have conceived of 
the true system of the world as early as 1507. He devoted the 
years of his middle life to the observations and computations 
necessary to the perfection of his system, and communicated 
his views to a few friends, but long refused to publish them. 
fearing the popular prejudice which might thus be excited. 
In 1540, a brief statement of them was published by his friend 
Rheticus; and, as this was favorably received, he soon con- 
sented to the publication of his great work. The first printed 
copy was placed in his hands only a few hours before hie 
death, which occurred in May, 1543. 

The fundamental principles of the Copernican system are 
embodied in two distinct propositions, which have to be proved 
separately, and one of which might have been true without 
the other being so. They are as follows : 

1. The diurnal revolution of the heavens is only an appar- 
ent motion, caused by a diurnal revolution of the earth on an 
axis passing through its centre. 

2. The earth is one of the planets, all of which revolve 
round the sun as the centre of motion. The true centre of 
the celestial motions is therefore not the earth, but the sun. 
For this reason the Copernican system is frequently spoken of 
in historical discussions as the " heliocentric theory." 

The first proposition is the one with the proof of which Co- 
pernicus begins. He explains how an apparent motion may 
result from a real motion of the person seeing, as well as from 
a motion of the object seen, and thus shows that the diurnal 



54 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

motion may be accounted for just as well by a revolution of 
the earth as by one of the heavens. To sailors on a ship sail- 
ing on a smooth sea, the ship, and every thing in it, seems to be 
at rest and the shore to be in motion. Which, then, is more 
likely to be in motion, the earth or the whole universe outside 
of it? In whatever proportion the heavens are greater than 
the earth, in the same proportion must their motion be more 
rapid to carry them round in twenty -four hours. Ptolemy 
himself shows that the heavens were so immense that the 
earth was but a point in comparison, and, for any thing that 
is known, they may extend into infinity. Then we should re- 
quire an infinite velocity of revolution. Therefore, it is far 
more likely 'that it is this comparative point that turns, and 
that the universe is fixed, than the reverse. 

The second principle of the Copernican system — that the 
apparent annual motion of the sun among the stars, described 
in § 3 of the preceding chapter, is really due to an annual revo- 
lution of the earth around the sun — rests upon a very beautiful 
result of the laws of relative motion. This movement of the 
earth explains not only this apparent revolution of the sun, 
but the apparent epicyclic motion of the planets described in 
treating of the Ptolemaic system. 

In Fig. 15, let 8 represent the &\m,ABCD the orbit of the 
earth around it, and the figures 1, 2, 3, 4, 5, 6, six successive 
positions of the earth. These positions would be about two 
weeks apart. Also, let EFGH represent the apparent sphere 
of the fixed stars. Then, an observer at 1, viewing the sun in 
the direction 18, will see him as if he were in the celestial 
sphere at the point 1/, because, having no conception of the 
actual distance, the sun will appear to him as if actually among 
the stars at V which lie in the same straight line with him. 
When the earth, with the observer on it, reaches 2, he will see 
the sun in the direction 2#2', that is, as if among the stars in 
2'. That is, during the two weeks' interval, the sun will ap- 
parently have moved among the stars by an angle equal to the 
actual angular motion of the earth around the sun. So, as the 
earth passes through the successive positions 3, 4, 5, 6, the sun 



COPERNICUS. 



55 



will appear in the positions 3', 4' ', 5', 6', and the motion of the 
earth continuing all the way round its orbit, the sun will ap- 
pear to move through the entire circle EFGIL Thus we 
have, as a result of the annual motion of the earth around the 
sun, the annual motion of the sun around the celestial sphere 
already described in the third section of the preceding chapter. 




Fig. 15.— Apparent annual motion of the sun explained. 

Let us now see how this same motion abolishes the compli- 
cated system of epicycles by which the ancient astronomers 
represented the planetary motions. A theorem on which this 
explanation rests is this : If an observer in unconscious mo- 
tion sees an object at rest, that object will seem to him to be 
moving in a direction opposite to his own, and with an equal 
velocity. A familiar instance of this is the apparent motion 



56 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 



J 



e,' 



\ 



of objects on shore to passengers on a steamer. In Fig. 16, 
let ns suppose an observer on the earth carried around the 

sun Sin the orbit APCDEF, 
but imagining himself at rest 
in the centre of motion S. Sup- 
pose that he observes the ap- 
parent motion of the planet P, 
which is really at rest. How 
will the planet appear to move ? 
To show this, we represent ap- 
parent directions and motions 
by dotted lines. Let us begin 
with the observer at A, from 
which position he really sees 
the planet in the direction and 
distance AP. But, imagining 
himself at S, he thinks he sees 
the planet at the point a, the 
distance and direction of which 
Sa is the same with AP. As 
p he passes unconsciously from A 
to P, the planet seems to him to 
move past from a to b in the op- 
posite direction; and, still think- 
ing himself at rest in S, he sees 
the planet in b, the line Sb be- 
Fro. 16.-Showing how the apparent epi- j n ~ equa J ail( j para U e l to PP. 
cyclic motion of the planets is accounted . , , « 

for by the motion of the earth round the As he recedes from the plan- 

sun " et through the arc BCD, the 

planet seems to recede from him through bed. While he 
moves from left to right through DP, the planet seems to 
move from right to left through de. Finally, as he approaches 
the planet through the arc EFA, the planet will seem to ap- 
proach him through efa, and when he gets back to A he 
will locate the planet at a, as in the beginning. Thus, in 
consequence of the motion of the observer around the circle 
ABCDEF, the planet, though really at rest, will seem to him 




COPEEXICUS. 57 

to move through a corresponding circle, abcdef. If there are 
a number of planets, they will all seem to describe correspond- 
ing circles of the same magnitude. 

If the planet P, instead of being at rest, is in motion, the 
apparent circular motion will be combined with the forward 
motion of the planet, and the latter will now describe a circle 
around a centre which is in motion. Thus we have the appar- 
ent motion of the planets around a moving centre, as already 
described in the Ptolemaic system. We have said, in § 7 of 
the preceding chapter, that by this system the motions of the 
planets are represented by supposing a fictitious planet to re- 
volve around the heavens with a regular motion, while the 
real planet revolves around this fictitious one as a centre once 
a year. Here, the progressive motion of the fictitious planet 
is (in the case of the outer planets Mars, Jupiter, and Sat- 
urn) the motion of the real planet around the sun, while the 
circle which the real planet describes around this mo ring cen- 
tre is only an apparent motion due to the observer being car- 
ried around the sun on the earth. If the reader will com- 
pare the epicyclic motion of Ptolemy, represented in Figs. 1" 
and 11 with the motion explained in Fig. 16, he will find that 
they correspond in every particular. In the case of the inner 
planets, Mercury and Venus, which never recede far from the 
sun, the epicyclic motion by which they seem to vibrate from 
one side of the sun to the other is due to their orbital motion 
around the sun, while the progressive motion with which they 
follow the sun is due to the revolution of the earth around 
the sun. 

We may now see clearly how the retrograde motion and 
stationary phases of the planets are explained on the Coper- 
nican system. The earth and all the planets are really mov- 
ing round the sun in a direction which we call east on the 
celestial sphere. When the earth and an outer planet are 
on the same side of the sun, they are moving in the same 
direction ; but the earth is moving faster than the planet. 
Hence, to an observer on the earth, the planet seems to be 
moving west, though its real motion is east. As the earth 



58 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

passes to the opposite side of the sun from the planet, it 
changes its motion to a direction the opposite of that of the 
planet, and thus the westerly motion of the latter appears to 
be increased by the whole motion of the earth.* Between 
these two motions there is a point at which the planet does 
not seem to move at all. This is called the stationary point. 
If the planet we consider is not an outer, but an inner one, 
Mercury or Venus, and we view it when between us and the 
sun, its motion to us is reversed, because we see it from the 
side opposite the sun. Hence it seems to move west to us, 
and it is retrograde. The earth is indeed moving in the same 
real direction; but since the planet moves faster than the 
earth, its retrograde motion seems to predominate. As the 
planet passes round in its orbit, it first appears stationary, 
and then, passing to the opposite side of the sun, it seems 
direct. 

Let us now dwell for a moment on some considerations 
which will enable us to do justice to the Ptolemaic system, as 
it is called, by seeing how necessary a step it was in the evo- 
lution of the true theory of the universe. The great merit of 
that system consisted in the analysis of the seemingly compli- 
cated motions of the planets into a combination of two circular 
motions, the one that of a fictitious planet around the celestial 
sphere, the other that of the real planet around the fictitious 
one. Without that separation, the constant oscillations of the 
planets back and forth could not have suggested any idea 
whatever, except that of a motion too complicated to be ex- 
plained on mechanical principles. But when, leaving out of 
sight the regular forward motion of the mean or fictitious 
planet, the attention was directed to the epicyclic motion 
alone, one could not fail to see the remarkable correspondence 
between this latter motion and the apparent annual motion 
of the sun. Seeing this, it took a very small step to see that 

* It must not be forgotten that the direction east in the heavens is a curved di- 
rection, as it were, and is opposite on opposite sides of the sun or celestial sphere. 
For instance, the motions of the stars as they rise and as they set are opposite, 
but both are considered west. 



COPERNICUS. 59 

the sun, and not the earth, was the centre of planetary motion. 
Then nothing but the illusions of sense remained to prevent 
the acceptance of the theory that the earth was itself a planet 
moving round the sun, and that both the annual motion of the 
sun and the epicyclic motion of the planets were not real, but 
apparent motions, due to the motion of the earth itself; and 
in no other way than this could the heliocentric theory have 
been developed. 

The Copernican system affords the means of determining 
the proportions of the solar system, or the relative distances of 
the several planets, with great accuracy. That is, if we take 
as our measuring- rod the distance of the earth from the sun, 
we can determine how many lengths of this rod, or what frac- 
tional parts of its length, will give the distance of each planet. 
although the length of the rod itself may remain unknown. 
This determination rests on the principle that the apparent 
circle or epicycle described by the planet in Fig. 16 is of the 
same magnitude with the actual orbit described by the earth 
around the sun. Hence, the nearer the observer is to this cir- 
cle, the larger it will appear. The apparent epicycle described 
by Neptune is rather less than two degrees in radius ; that is, 
the true planet Neptune is seen to swing a little less than two 
degrees on each side of its mean position in consequence of 
the annual motion of the earth round the sun. This shows 
that the orbit of the earth, as seen from Xeptune, subtends an 
angle of only two degrees. On the other hand, the planet 
Mars generally swings more than 40° on each side; sometimes, 
indeed, more than 45°. From this a trigonometrical calcula- 
tion shows that its mean distance is only about half as much 
again as that of the earth ; and the fact that the apparent 
swing is variable shows the distance to be different at different 
times. 

As it will be of interest to see how nearly Copernicus was 
able to determine the distances of the planets, we present his 
results in the following table, together with what we now 
know to be the true numbers. The numbers given are deci- 
mal fractions, expressing the least and greatest distance of 



60 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

each planet from the sun, the distance of the earth being taken 
as unity.* 



Planets. 


Least Distance. 


Greatest Distance. 


Copernicus. 


Moderu. 


Copernicus. 


Modern. 


Mercury 

Venus 

Mars 

Jupiter 

Saturn 


0.326 
0.709 
1.373 
4.980 
8.66 


0.308 
0.718 
1.382 
4.952 
9.00 


0.405 
0.730 
1.666 
5.453 
9.76 


0.467 
0.728 
1.666 
5.454 
10.07 



Considering the extremely imperfect means of observation 
which the times afforded, these results of Copernicus come 
very near the truth. The greatest proportional deviation is in 
the case of Mercury, the most difficult of all the planets to 
observe, even to the present day. It is said that Copernicus 
died without ever seeing this planet. 

The eccentricities of the orbits were represented by Coper- 
nicus in a way which agrees exactly with the modern formulae 
when only a rough approximation is sought for. Like Ptole- 
my, he supposed the orbits of the planets not to be centred on 
the sun, but to be displaced by a small quantity termed the 
eccentricity. But it had long been known that the theory of 
uniform motion in an eccentric circle, though it might make 
the irregularities in the planet's angular motion come out all 
right, would make the changes of distance double their true 
value. He therefore took for the eccentricity a mean between 
that which would satisfy the motion in longitude, and that 
which would give the changes of distance, and added a small 
epicycle of one-third this eccentricity ; and, by supposing the 
planet to make two revolutions in this epicycle for every 
revolution around the sun, he represented both irregulari- 
ties.f 

* I have deduced these numbers from the tables given in Book V. of "De 
Revolutionibus Orbium Ccelestium." They are probably the most accurate that 
Copernicus was able to obtain. 

f The mathematical form of this theory of Copernicus is as follows : Putting 



OBLIQUITY OF THE ECLIPTIC. 61 

The work of Copernicus was the greatest step ever taken in 
astronomy. But he still took little more than the single Btep 
of showing what apparent motions in the heavens were real. 
and what were due to the motion of the observer. Not only 
was his work in other respects founded on that of Ptolemy, 
but he had many of the notions of the ancient philosophy re- 
specting the fitness of things. Like Ptolemy, he thought the 
heavens as well as the earth to be spherical, and all the celes- 
tial motions to be circular, or composed of circles. He argues 
against Ptolemy's objections to the theory of the earth's mo- 
tion, that that philosopher treats of it as if it were an enforced 
or violent motion, entirely forgetting that if it exists it must 
be a natural motion, the laws of which are altogether different 
from those of violent motion. Thus, part of his argument was 
really without scientific foundation, though his conclusion was 
correct. Still, Copernicus did about all that could have been 
done under the circumstances. His hypothesis of a small epi- 
cycle one-third the eccentricity represented the motions of the 
planets around the sun with all the exactness that observation 
then admitted of, while, in the absence of any knowledge of 
the laws of motion, it was impossible to frame any dynamical 
basis for the motions of the planets. 

§ 2. Obliquity of the Ecliptic / Seaso?is, etc. ; on the Cojitr- 
nican System. 

We have next to explain the relations of the ecliptic and 
equator on the new system. Since, on this system, the ce- 
lestial sphere does not revolve at all, what is the significance 
of the pole and axis around which it seems to revolve ? The 

e for his eccentricity, and g for the mean anomaly of the planet, he represented its 
rectangular coordinates in the form 

x = a (cos. g — e + ^e cos. 2g), 

y - a (sin. g + ±e sin. 2g) ; 

while the approximate modern formulae of the elliptic motion are — 
x = a (cos. g — \e + \e cos. 2g), 
y = a (sin. g + U sin. 2#), 



62 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

answer is, that the celestial poles are the points among the stars 
towards which the axis of the earth is directed. Here the 
stars are supposed to be infinitely distant, and the axis of the 
earth to be continued in an infinite straight line to meet them. 
Since this point appears to the unassisted sight to be the same 
during the entire year, it follows that as the earth moves round 
the sun, its axis keeps pointing in the same absolute direction, 
as will be shown in Fig. 18. But in the preceding chapter we 
showed that there is a slow but constant change in the position 
of the pole among the stars, called precession, which the an- 
cient astronomers discovered by studying observations extend- 




Fig. 17.— Relation of the terrestrial and celestial poles and equators. 

ing through several centuries, and this shows that on the Co- 
pernican system the direction of the earth's axis is slowly 
changing. 

To. conceive of the celestial equator on the Copernican sys- 
tem, we must imagine the globular earth to be divided into 
two hemispheres by a plane intersecting the earth around its 
equator, and continued out on all sides till it reaches the ce- 
lestial sphere. This may, perhaps, be better understood by 
referring to Fig. 17, representing the earth in the centre of the 



OBLIQUITY OF THE ECLIPTIC. 63 

imaginary celestial sphere. The dotted lines passing from the 
poles of the earth to the points P and 8 mark the poles of that 
sphere. It is evident that as the earth turns on this axis, the 
celestial sphere, no matter how great it may seem to be, will 
appear to turn on the same axis in the opposite direction. 
Again, ep being the earth's equator, dividing it into two equal 
parts, we have only to imagine it to be extended to jETand Q. 
all round the celestial sphere, to cut the latter into two equal 
parts. 

Let us next examine more closely the relation of the earth 
to the sun. We have already shown that as the earth moves 
around the sun, the latter seems to move around the celestial 
sphere, and the circle in which he seems to move is called the 
ecliptic. But the ecliptic and the celestial equator are in- 
clined to each other by an angle of about 23£ G . This shows 
that the axis of the earth is not perpendicular to its orbit, but 




° D 

Fig. IS.— Causes of change? of seasons on the Copemican system. 

is inclined 23^° to that perpendicular, as shown in Fig. 18, 
which represents the annual course of the earth round the 
sun. It is of necessity drawn on a very incongruous scale, 
because the distance of the sun from the earth being near- 
ly 12,000 diameters of the latter and 110 that of the sun, both 
bodies would be almost invisible if they were not greatly mag- 
nified in the figure. A difficulty which may suggest itself is, 
that the present figure represents the earth as moving away 

6 



64: SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

from its position in the centre of the sphere. There are two 
ways of avoiding this difficulty. One is to suppose that the 
observer carries the imaginary celestial sphere with him as he 
is carried around the sun; the other is to consider the sphere 
as nearly infinite in diameter. The latter is probably the 
easiest mode of conception for the general reader. He must, 
therefore, in the last figure suppose the sphere to extend out 
to the fixed stars, which are so distant that the whole orbit of 
the earth is but a point in comparison ; and the different points 
of the sphere towards which the poles and the equator of the 
earth point, as the latter moves round the sun, are so far as to 
appear always the same. It now requires but an elementary 
idea of the geometry of the sphere to see that these two great 
circles of the celestial sphere — the ecliptic, around which the 
sun seems to move, and the equator, which is everywhere 
equally distant from the points in which the earth's axis in- 
tersects the sphere — will appear inclined to each other by the 
same angle by which the earth's axis deviates from the per- 
pendicular to the ecliptic. 

Next, we have to see how the changes of the seasons, the 
equinoxes, etc., are explained on the Copernican theory. In 
the last figure the earth is represented in four different posi- 
tions of its annual orbit around the sun. In the position A, 
the south pole is inclined 23^° towards the sun, while the 
north pole, and the whole region within the arctic circle, is 
enveloped in darkness. Hence, in this position, the sun nei- 
ther rises to the inhabitants of the arctic zone, nor sets to 
those of the antarctic zone. Outside of these zones, he rises 
and sets, and the relative lengths of day and night at any 
place can be estimated by studying the circles around which 
that place is carried by the diurnal turning of the earth on its 
axis. To facilitate this, we present on the following page a 
magnified picture of the earth at A, showing more fully the 
hemisphere in which it is day and that in which it is night. 
The seven nearly horizontal lines on the globe are examples 
of the circles in question. We see that a point on the arctic 
circle just grazes the dividing-line between light and darkness 



THE SEASONS. 



65 




once in its revolution, or once a day; that is, the sun just 
shows himself in the horizon once a day. Of the next circle 
towards the south about two- 
thirds is in the dark, and one- 
third in the light hemisphere. 
This shows that the nighta are 
about twice as long as the 
days. This circle is near that 
around which London is carried 
by the diurnal revolution of the 
earth on its axis. As we go 
south, we see that the propor- 
tion of light on the diurnal cir- 
cles constantly increases, while FMk m.-Mmi* *•" <* ^e enrth in 

" ..... the position A of the preceding rk'nre, 

that of darkness dimini&hes, nil- showing winter in the northern hemi- 

til we reach the equator, where sphere ' a,ld BOminer ta lhe -» thern - 
they are equal. When we pass into the southern hemisphere, 
we see the light covering more than half of each circle, the 
proportion of light to darkness constantly increasing, at the 
same rate that the opposite proportion would increase in going 
to the north. When we reach the antarctic circle, the whole 
circle is in the light hemisphere, the observer just grazing the 
dividing-line at midnight. Inside of that circle the observer 
is in sunlight all the time, so that the snn does not set at all. 
We see, then, that at the equator the days and nights are al- 
ways of the same length, and that the inequality increases 
we approach either pole. 

We now go on three months to the position Z>. which the 
earth occupies in March. Here the plane of the terrestrial 
equator being continued, passes directly through the sun ; the 
latter, therefore, seems to be in the celestial equator. All the 
diurnal circles are here one-half in the illuminated, and one- 
half in the unilluminated hemisphere, the latter being invisi- 
ble in the figure, through its bein^ behind the earth. The 
days and nights are, therefore, of equal length all over the 
globe, if we call it night whenever the sun is geometrically 
below the horizon. In the position C, which the earth takes 



(jQ SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

in June, everything is the same as in position A, except that 
effects are reversed in the two hemispheres. The northern 
hemisphere now has the longest days, and the southern one 
the longest nights. At D, which the earth reaches in Sep- 
tember, the days and nights are equal once more, for the same 
reason as in B. Thus, all the seemingly complicated phenom- 
ena which we have described in the preceding chapter are 
completely explained in the simplest way on the new system. 
We have next to see how the details of the system were filled 
in by the immediate successors of Copernicus. 

§ 3. Tycho Brake. 

We have said that no great advance could be made upon 
the Copernican system, without either a better knowledge of 
the laws of motion or more exact observations of the positions 
of the heavenly bodies. It was in the latter direction that 
the advance was first made. The leader was Tycho Brahe, 
who was bora in 1546, three years after the death of Coperni- 
cus. His attention was first directed to the study of astron- 
omy by an eclipse of the snn on August 21st, 1560, which was 
total in some parts of Europe. Astonished that such a phe- 
nomenon could be predicted, he devoted himself to a study of 
the methods of observation and calculation by which the pre- 
diction was made. In 1576 the King of Denmark founded 
the celebrated Observatory of IJraniberg, at w T hich Tycho 
spent twenty years, assiduously engaged in observations of the 
positions of the heavenly bodies with the best instruments that 
could then be made. This was just before the invention of 
the telescope, so that the astronomer could not avail himself 
of that powerful instrument. Consequently, his observations 
were superseded by the improved ones of the centuries fol- 
lowing, and their celebrity and importance are principally due 
to their having afforded Kepler the means of discovering his 
celebrated laws of planetary motion. 

As a theoretical astronomer, Tycho was unfortunate. He 
rejected the Copernican system, for a reason which, in his day, 
had some force, namely, the incredible distance at which it 



TYCHO BRAHE. 67 

was necessary to suppose the fixed stars to be situated if that 
system were accepted. We have shown how, on the Coperni- 
can system, the outer planets seem to describe an annual revo- 
lution in an epicycle, in consequence of the annual revolution 
of the earth around the sun. The fixed stars, which are sit- 
uated outside the solar system, must appear to move in the 
same way, if the system be correct. But no observations, 
whether of Tycho or his predecessors, had shown any such 
motion. To this the friends of Copernicus could only reply 
that the distance of the fixed stars must be so great that the 
motion could not be seem Since a vibration of three or four 
minutes of arc might have been detected by Tycho. it would 
be necessary to suppose the stellar sphere at least a thousand 
times the distance of the sun, and a hundred times that of S 
urn, then the outermost known planet. That a space so vast 
should intervene between the orbit of Saturn and the fixed 
stars seemed entirely incredible: to the philosophers of the 
day it was an axiom that nature would not permit the waste of 
space here implied. At the same time, the proofs given by 
Copernicus that the sun was the centre of the planetary mo- 
tions were too strong to be overthrown. Tycho, therefore, 
adopted a system which was a compound of the Ptolemaic 
and the Copernican ; he supposed the five planets to move 
around the sun as the centre of their motions, while the sun 
was itself in motion, describing an annual orbit around the 
earth, which remained at rest in the centre of the universe. 

Perhaps it is fortunate for the reception of the Copernican 
system that the astronomical instruments of Tycho were not 
equal to those of the beginning of the present century. Had 
he found that there was no annual parallax among the stars 
amounting to a second of arc, and therefore that, if Coperni- 
cus was right, the stars must be at least 200,000 times the dis- 
tance of the sun, the astronomical world might have stood 
aghast at the idea, and concluded that, after all, Ptolemy must 
be right, and Copernicus wrong. 

Tycho never elaborated his system, and it is hard to say 
how he would have answered the numerous objections to it. 



GS ststem of the world historically developed. 

He never had any disciples of eminence, except among the 
ecclesiastics ; in fact, the invention of the telescope did away 
with the last remaining doubts of the correctness of the Co- 
pernican system before a new one would have had time to 
gain a foothold. 

§ 4. Kepler. — His Laws of Planetary Motion. 

Kepler was born in 1571, in Wiirtemberg. He was for a 
while the assistant of Tycho Brahe in his calculations, but was 
too clear-sighted to adopt the curious system of his master. 
Seeing the truth of the Copernican system, he set himself to 
determine the true laws of the motion of the planets around 
the sun. We have seen that even Copernicus had adopted the 
ancient theory, that all the celestial motions are compounded 
of uniform circular motions, and had thus been obliged to in- 
troduce a small epicycle to account for the irregularities of 
the motion. The observations of Tycho were so much more 
accurate than those of his predecessors, that they showed Kep- 
ler the insufficiency of this theory to represent the true mo- 
tions of the planets around the sun. The planet most favora- 
ble for this investigation was Mars, being at the same time 
one of the nearest to the earth, and one of which the orbit 
was most eccentric. The only way in which Kepler could 
proceed in his investigation was to make various hypotheses 
respecting the orbit in which the planet moved, and its velocity 
in various points of its orbit, and from these hypotheses to cal- 
culate the positions and motions of the planet as seen from 
the earth, and then compare with observations, to see whether 
the observed and calculated positions agreed. As our modern 
tables of logarithms by which such calculations are immensely 
abridged were not then in existence, each trial of an hypothe- 
sis cost Kepler an immense amount of labor. Finding that 
the form of the orbit was certainly not circular, but elliptical, 
he was led to try the effect of placing the sun in the focus of 
the ellipse. Then, the motion of the planet would be satisfied 
if its velocity were made variable, being greater the nearer 
it was to the sun. Thus he was at length led to the first two 






KEPLER. 69 

of liis three celebrated laws of planetary motion, which are as 
follows : 

1. The orbit of each planet is an ellipse, having the sun in 
one focus. 

2. As the planet moves round the sun, its radius-vector (or 
the line joining it to the sun) passes over equal areas in 
equal times. 

To explain these laws, let PA (Fig. 20) be the ellipe 
which the planet moves. Then the sun will not be in the cen- 




Fig. 20.— Illustrating Kepler's first two laws of planetary motion. 

tre of the ellipse, but in one focus, say at S, the other focus 
being empty. When the planet is at P. it is at the point near- 
est the sun; this point is therefore called the perihelion. As 
it passes round to the other side of the sun, it continues to re- 
cede from him till it reaches the point A, when it attains its 
greatest distance. This point is the aphelion. Then it begins 
to approach the sun again, and continues to do so till it reaches 
P once more, when it again begins to repeat the same orbit. 
It thus describes the same ellipse over and over. 

Now, suppose that, starting from P, we mark the position 
of the planet in its orbit at the end of any equal intervals of 
time, say 30 days, 60 days, 90 days, 120 days, and so on. Let 
«, b, c, d be the first four ©f these positions between each of 
which the planet has required 30 days to move. Draw lines 
from each of the five positions of the planet, beginning at P. 



70 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 



to the sun at S. We shall thus have four triangular spaces, 
over each of which the radius-vector of the planet has swept 
in 30 days. The first of Kepler's laws means that the areas 
of all of these spaces will be equal. 

The old theory that the motions of the heavenly bodies must 
be circular and uniform, or, at least, composed of circular and 
uniform motions, was thus done away with forever. The el- 
lipse took the place of the circle, and a variable motion the 
place of a uniform one. 

Another law of planetary motion, not less important than 
these two, was afterwards discovered by Kepler. Copernicus 
knew, what had been surmised by the ancient astronomers, 
that the more distant the planet, the longer it took it to per- 
form its course around the sun, and this not merely because it 
had farther to go, but because its motion was really slower. 
For instance, Saturn is about 9^ times as far as the earth, and 
if it moved as fast as the earth, it would perform its revolu- 
tion in 9J years ; but it actually requires between 29 and 30 
years. It does not, therefore, move one-third so fast as the 
earth, although it has nine times as far to go. Copernicus, 
however, never detected any relation between the distances 
and the periods of revolution. Kepler found it to be as fol- 
lows: 

Third law of planetary motion. The square of the time 
of revolution of each planet is proportional to the cube of 
its mean distance from the sun. 

This law is shown in the following table, which gives (1) 
the mean distance of each planet known to Kepler, expressed 
in astronomical units, each unit being the mean distance of 



Planets. 


(1) 
Distance. 


(2) 
Cube of Dis- 
tance. 


(3) 
Period 

(Years). 


(4) 

Square of 

Period. 


Mercurv 


0.387 
0.723 
1.000 
1.524 
5.203 
9.539 


0.058 
0.378 
1.000 

• 3.540 

140.8 

868.0 


0.241 
0.615 
1.000 

1.881 
11.86 
29.46 


0.058 
0.378 
1.001 
3.538 

140.66 

867.9 
. 


Ven us 


Earth 

Mars 

Jupiter 

Saturn 



FROM KEPLER TO NEWTON. 71 

the earth from the sun ; (2) the cube of this quantity ; (3) the 
time of revolution in years; and (4) the square of this time. 

The remarkable agreement between the second and fourth 
columns will be noticed. 

§ 5. From Kepler to Neioton. 

So far as the determination of the laws of planetary motion 
from observation was concerned, we might almost say that 
Kepler left nothing to be done. Given the position and 
magnitude of the elliptic orbit in which any planet moved, 
and the point of the orbit in which it was found at any 
date, and it became possible to calculate the position of the 
planet in all future time. More than that science could not 
do. It is true that the places of the planet thus predicted 
were not found to agree exactly with observation; and had 
Kepler had at his command observations as accurate as those 
of the present day, he would have found that his laws could 
not be made to perfectly represent the motion of the planets. 
Not only would the elliptic orbit have been found to vary 
position from century to century, but the planets would have 
been found to deviate from it, first in one direction and then 
in the other, while the areas described by the radius- vector 
would have been sometimes larger and sometimes smaller. 
"Why should a planet move in an elliptic orbit \ Why should 
its radius- vector describe areas proportional to the time? 
Why should there be that exact relation between their dis- 
tances and times of revolutions? Until these questions were 
answered, it would have been impossible to say why the plan- 
ets deviated from Kepler's laws; and they were questions 
which it was impossible to answer until the general laws of 
motion, unknown in Kepler's time, were fully understood. 

The first important step in the discovery of these laws was 
taken by Galileo, the great contemporary of Kepler, one of 
the inventors of the telescope, and the first who ever pointed 
that instrument at the heavens. From a scientific point of 
view, as inventor of the telescope, founder of the science of 
dynamics, teacher and upholder of the Copernican system, and 



72 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 

sufferer at the hands of the Inquisition, for promulgating what 
he knew to be the truth, Galileo is perhaps the most interest- 
ing character of his time. If any serious doubt could remain 
of the correctness of the Copernican system, it was removed 
by the discoveries made by the telescope. The phases of 
Yen us showed that she was a dark globular body, like the 
earth, and that she really revolved around the sun. In Jupi- 
ter and his satellites, the solar system, as described by Coperni- 
cus, was repeated on a small scale w T ith a fidelity which could 
not fail to strike the thinking observer. There was no longer 
any opposition to the new doctrines from any source entitled 
to respect. The Inquisition forbade their promulgation as 
absolute truths, but were perfectly willing that they should be 
used as hypotheses, and rather encouraged men of science in 
the idea of investigating the interesting mathematical prob- 
lems to which the explanation of the celestial motions by the 
Copernican system might give rise. The only restriction was 
that they must stop short of asserting or arguing the hypothe- 
ses to be a reality. As this assertion was implicitly contained 
in several places in the great work of Copernicus, they con- 
demned this work in its original form, and ordered its revi- 
sion.* Probably the decree of the Inquisition was entirely 
without effect in stopping the reception of the Copernican 
system outside of Italy and Spain. 

It will be seen, from what has been said, that the next step 
to be taken in the direction of explaining the celestial motions 
must be the discovery of some general cause of those motions, 
or, at least, their reduction to some general law. The first 
attempt to do this was made by Descartes in his celebrated 
theory of vortices, which for some time disputed the field with 
Newton's theory of gravitation. This philosopher supposed 
the sun to be immersed in a vast mass of fluid, extending in- 
definitely in every direction. The sun, by its rotation, set the 

* The order for this revision was made at the time of condemning Galileo's 
work, but I am not aware that it was ever executed. An edition of Copernicus, 
revised to satisfy the Inquisition, would certainly be an interesting work to the 
astronomical bibliopole at the present time. 



FROM KEPLER TO NEWTON. 73 

parts of the fluid next to it in rotation ; these communicated 
their motions to the parts still farther out, and so on, until 
the whole mass was set in rotation like a whirlpool. The 
planets were carried around in this ethereal whirlpool. The 
more distant planets moved more slowly because the ether 
was less affected by the rotation of the sun the more distant 
it was from him. In the great vortex of the solar system 
were smaller ones, eacli planet being the centre of one ; and 
thus the satellites, floating in the ether, were carried round 
their primaries. Had Descartes been able to show that the 
parts of his vortex must move in ellipses having the sun in 
one focus, that they must describe equal areas in equal times, 
and that the velocity must diminish as we recede from the 
sun, according to Kepler's third law, his theory would so far 
have been satisfactory. Failing in this, it cannot be regarded 
as an advance in science, but rather as a step backwards. Yet. 
the great eminence of the philosopher and the n amber of his 
disciples secured a wide currency for his theory, and we And 
it supported by no less an authority than John Bernoulli. 

After Galileo, the man who, perhaps, did most to prepare 
the way for gravitation was Iluyghens. As a mathematician, 
a mechanician, and an observer, he stood in the first rank. 
He discovered the laws of centrifugal force, and if he had 
simply applied these laws to the solar system, he would have 
been led to the result that the planets are held in their orbits 
by a force varying as the inverse square of their distance from 
the sun. Having found this, the road to the theory of gravita- 
tion could hardly have been missed. But the great discovery 
seemed to require a mind freshly formed for the occasion. 



74 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 



CHAPTER III. 

UNIVERSAL GRAVITATION. 

§ 1. Newton.- — Discovery of Gravitation. 

The real significance of Newton's great discovery of univer- 
sal gravitation is fully appreciated by but few. Gravitation 
is generally thought of as a mysterious force, acting only be- 
tween the heavenly bodies, and first discovered by Newton. 
Had gravitation itself been discovered by Newton as some 
new principle to account for the motions of the planets, it 
would not have been so admirable a discovery as that which 
he actually made. Gravitation, in a somewhat limited sphere, 
is known to all men. It is simply the force which causes 
all heavy bodies to fall, or to tend towards the centre of the 
earth. Every one who had ever seen a stone fall, or felt it to 
be heavy, knew of the existence of gravitation. What New- 
ton did was to show that the motions of the planets were 
determined by a universal force, of which the force w T hich 
caused the apple to fall was one of the manifestations, and 
thus to deprive the celestial motions of all the mystery in 
which they had formerly been enshrouded. To his predeces- 
sors, the continuous motion of the planets in circles or ellipses 
w T as something so completely unlike any motion seen on the 
surface of the earth, that they could not imagine it to be gov- 
erned by the same laws ; and, knowing of no law to limit the 
planetary motions, the idea of the heavenly bodies moving in 
a manner w T hich set all the laws of terrestrial motion at de- 
fiance was to them in no way incredible. 

The idea of a cosmical force emanating from the sun or the 
earth, and causing the celestial motions, did not originate with 
Newton. We have seen that even Ptolemy had an idea of a 
force which, always directed towards the centre of the earth, 



XEWTOX.— DISCOVERY OF GRAVITATIOX. 75 

or, which was to him the same thing, towards the centre of 
the universe, not only caused heavy bodies to fall, but bound 
the whole universe together. Kepler also maintained that the 
force which moved the planets resided in, and emanated from, 
the sun. But neither Ptolemy nor Kepler could give any ade- 
quate explanation of the force on the basis of laws seen in ac- 
tion around us; nor was it possible to form any conception of its 
true nature without a knowledge of the general laws of motion 
and force, to which neither of these philosophers ever attained. 

The great misapprehension which possessed the minds of 
nearly all mankind till the time of Galileo was, that the con- 
tinuous action of some force was necessary to keep a moving 
body in motion. That Kepler himself was fully possessed of 
this notion is shown by the fact that he conceived a force act- 
ing only in the direction of the sun to be insufficient for keep- 
ing up the planetary motions, and to require to be supplement- 
ed by some force which should constantly push the planet 
ahead. The latter force, he conceived, might arise from the 
rotation of the sun on his axis. It is hard to say who was the 
first clearlv to see and announce that this notion was entirely 
incorrect, and that a body once set in motion, and acted on by 
no force, would move forwards forever — so gradually did the 
great truth dawn on the minds of men. It must have been 
obvious to Leonardo da Vinci ; it was implicitly contained in 
Galileo's law of falling bodies, and in Iluvghens's theory of 
central forces; yet neither of these philosophers seems to have 
clearlv and completely expressed it. "We can hardly be far 
wrong in saying that Xewton was the first who clearly laid 
down this law in connection with the correlated laws which 
cluster around it. The basis of Xewton's discovery were these 
three laws of motion : 

First law. A body once set in motion and acted on by no force- 
will move forwards in a straight line and with a uniform velocity 
forever. 

Second law. If a moving body be acted on by any force, its de- 
viation from the motion defined in the first law ivill be in the direc- 
tion of the force, and proportional to it. 



76 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

Third law. Action and reaction are equal, and in opposite di- 
rections ; that is, whenever any one body exerts a force on a second 
one, the latter exerts a similar force on the first, only in the opposite 
direction. 

The first of these laws is the fundamental one. The cir- 
cumstance which impeded its discovery, and set man astray 
for many centuries, was that there was no body on the earth's 
surface acted on 03 7 no force, and therefore no example of a 
body moving in a continuous straight line. Every body on 
which an experiment could be made was at least acted on by 
the gravitation of the earth — that is, by its own weight — and, 
in consequence, soon fell to the earth. Other forces which im- 
peded its motion were friction and the resistance of the air. 
It needed research of a different kind from what the prede- 
cessors of Galileo had given to physical problems to show that, 
but for these forces, the body would move in a straight line 
without hinderance. 

We are now prepared to understand the very straightfor- 
ward and simple way in which Newton ascended from what 
lie saw on the earth to the great principle with which his 
name is associated. We see that there is a force acting all 
over the earth by w T hich all bodies are drawn towards the 
earth's centre. This force extends without sensible diminu- 
tion, not only to the tops of the highest buildings, but of the 
highest mountains. How much higher does it extend ? Why 
should it not extend to the moon ? If it does, the moon would 
tend to drop to the earth, just as a stone thrown from the 
hand does. Such being the case, why should not this simple 
force of gravity be the force which keeps the moon in her 
orbit, and prevents her from flying off in a straight line under 
the first law of motion ? To answer this question, it was nec- 
essary to calculate what force w T as requisite to retain the moon 
in her orbit, and to compare it with gravity. It was at that 
time well known to astronomers that the distance of the moon 
was sixty semidiameters of the earth. Newton at first sup- 
posed the earth to be less than 7000 miles in diameter, and 
consequently his calculations failed to lead him to the right 



\ i:\YTON.— DISCOVERY OF GRAVITAT10X. 77 

result. This was in 1665, when he was only twenty - three 
years of age. He laid aside his calculations for nearly twenty 
years, when, learning that the measures of Picard, in France, 
showed the earth to be one-sixth larger than he had supposed, 
he again took up the subject. He now found that the deflec- 
tion of the orbit of the moon from a straight line was such as 
to amount to a fall of sixteen feet in one minute, the same dis- 
tance which a body falls at the surface of the earth in one 
second. The distance fallen being as the square of the time, 
it followed that the force of gravity at the surface of the earth 
was 3600 times as great as the force which held the moon in 
her orbit. This number was the square of 60, which ezpree 
the number of times the moon is more distant than we are 
from the centre of the earth. Hence, the force which holdt 
moon in her orbit is the same as that which makes a stone fall only 
diminished in the inverse square of the distance from the centre of 
the earth. 

To the mathematician the passage from the gravitation of an 
apple to that of the moon is quite simple; but the non-mathe- 
matical reader may not, at first sight, see how the moon can he 
constantly falling towards the earth without ever becoming any 
nearer. The following illustration will make the matter clear : 
any one can understand the law of falling bodies, by which a 
body falls sixteen feet the first second, three times that distance 
the next, five times the third, and so on. If, in place of falling. 
the body be projected horizontally, like a cannon-ball, for ex- 
ample, it will fall sixteen feet out of the straight line in which 
it is projected during the first second, three times that distance 
the next, and so on, the same as if dropped from a state of 
rest. In the annexed figure, let A B' represent a portion of 
the curved surface of the earth, and AD a straight line hori- 
zontal at A, or the line along which an observer at A would 
sight if he set a small telescope in a horizontal position. 
Then, owing to the curvature of the earth, the surface will 
fall away from this line of sight at the rate of about eight 
inches in the first mile, twenty-four inches more in the second 
mile, and so on. In five miles the fall will amount to sixteen 



SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 



feet. In ten miles, in addition to this sixteen feet, three times 
that amount will be added, and so on, the law being the same 




Fig. 21.— Illustrating the fall of the moon towards the earth. 

with that of a falling body. Now, let A be a high steep 
mountain, from the summit of which a cannon-ball is fired in 
the horizontal direction CE. The greater the velocity with 
which the shot is fired, the farther it will go before it reaches 
the ground. Suppose, at length, that we should fire it with 
a velocity of five miles a second, and that it should meet with 
no resistance from the air. Suppose e to be the point on the 
line five miles from G. Since it would reach this point in one 
second, it follows, from the law of falling bodies just cited, 
that it will have dropped sixteen feet below e. But we have 
just seen that the earth itself curves away sixteen feet at this 
distance. Hence, the shot is no nearer the earth than when it 
was fired. During the next second, while the ball would go to 
E 1 it would fall forty-eight feet more, or sixty-four feet in all. 
But here, again, the earth has still been rounding off, so the 
distance DB is sixty-four feet. Hence, the ball is still no near- 
er the earth than when it was fired, although it has been drop- 
ping away from the line in which it was fired exactly like a 
falling body. Moreover, meeting with no resistance, it is still 
going on with undiminished velocity; and, just as it has been 
falling for two seconds without getting any nearer the earth, 
so it can get no nearer in the third second, nor in the fourth, 
nor in any subsequent second ; but the earth will constantly 
curve away as fast as the ball can drop. Thus the latter will 
pass clear round the earth, and come back to the first point G ) 



NEWTON.— DISCOVERY OF GRAVITATION 79 

from which it started, in the direction of the arrow, without 
any loss of velocity. The time of revolution will be about an 
hour and twenty-four minutes, and the ball will thus keep on 
revolving round the earth in this space of time. In other 
words, the ball will be a satellite of the earth, just like the 
moon, only much nearer, and revolving much faster. 

Our next step is to extend gravitation to other bodies than 
the earth. The planets move around the sun as the moon 
does around the earth, and must, therefore, be acted on by a 
force directed towards the sun. This force can be no other 
than the gravitation of the sun itself. A very simple calcula- 
tion from Kepler's third law shows that the force with which 
each planet thus gravitates towards the sun is inversely as the 
square of the mean distance of the planet. 

Only one more step is necessary. "What sort of an orbit 
will a planet describe if acted on by a force directed towards 
the sun, and inversely as the square of the distance '. A very 
simple demonstration will show that, no matter what the law 
of force, if it be constantly directed towards the sun, the radi- 
us-vector of the planet will sweep over equal areas in equal 
times. And, conversely, it cannot sweep over equal areas in 
equal times if the force acts in any other direction than that 
of the sun. Hence it follows, from Kepler's second law. that 
the force is directed towards the sun itself. 

The problem of determining what form of orbit would be 
described was one with which very few mathematicians of 
that day were able to grapple. New ton succeeded in proving, 
by a rigorous demonstration, that the orbit would be an el- 
lipse, a parabola, or a hyperbola, according to circumstances, 
having the sun in one of its foci, which, in the case of the 
ellipse, was Kepler's first law. Thus, all mystery disappeared 
from the celestial motions, and the planets were shown to be 
simply heavy bodies moving according to the same laws we 
see acting all around us, only under entirely different circum- 
stances. All three of Kepler's laws were expressed in the sin- 
gle law of gravitation towards the sun, with a force acting in- 
versely as the square of the distance. 

7 



80 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 

Very beautiful is the explanation which gravity gives of 
Kepler's third law. We have seen that if we take the cubes 
of the mean distances of the several planets, and divide them 
by the square of the times of revolution, the quotient will be 
the same for each planet of the system. If we proceed in the 
same way with the satellites of Jupiter, cubing the distance 
of each satellite from Jupiter, and dividing the cube by the 
square of the time of revolution, the quotient will be the same 
for each satellite, but will not be the same as for the planets. 
This quotient, in fact, is proportional to the mass or weight of 
the central body. In the case of the planets it is 1050 times 
as great as in the case of the satellites of Jupiter. This shows 
that the sun is 1050 times as heavy as Jupiter. We thus have 
a very convenient way of " weighing " such of the planets as 
have satellites, by measuring the orbits of the satellites, and 
determining the times of their revolution. But the weight is 
not thus expressed in tons, but only in fractions of the mass 
of the sun. 

The law, however, is not yet complete. The attraction be- 
tween the sun and planets must, by the third law of motion, 
be mutual. If the earth attracts the moon, she must, if the 
law be a general one, attract the planets also, and the planets 
must attract each other, and thus alter their motions around 
the sun. Now, it is known from observation that the planets 
do not move in exact accordance w T ith Kepler's laws. The 
final question, then, arises whether the attraction of the plan- 
ets on each other fully and exactly accounts for the deviations. 
This question Newton could answer only in an imperfect way, 
the problem being too intricate for his mathematics. He was 
able to show that the attraction of the sun would cause ine- 
qualities in the motion of the moon of the same nature as 
those observed, but he could not calculate their exact amount. 
Still, the general correspondence of his theory with the mo- 
tions of the heavens was so striking that there ought not to 
be any doubt of its truth. Very remarkable, therefore, is it 
to see the French Academy of Sciences, as late as 1732 — more 
than forty years later — awarding a prize to John Bernoulli, the 



GRAVITATION OF SMALL MASSES. 81 

celebrated mathematician, for a paper in which the motions 
of the planets were explained on the theory of vortices. Ir 
should not be inferred from this that that justly celebrated 
body still considered that theory to be correct ; but we may 
infer that they still considered it an open question whether 
the theory of gravitation was correct. 

To express Newton's theory with completeness, it is not suf- 
ficient to say simply that the sun, earth, and planets attract 
each other. Divide matter as finely as we may, we find ir 
still possessing the power of attraction, because it has weight 
Since the earth attracts the smallest particles, they must, by 
the third law T of motion, attract the earth with equal force. 
Hence we conclude that the power of attraction resides, not 
in the earth as a whole, but in each individual particle of the 
matter composing it; that is, the attraction of the earth upon 
a stone is simply the sum total of the attractions between the 
stone and all the particles composing the earth. 

There is no known limit to the distance to which the at- 
traction of gravitation extends. The attraction of the sun 
upon the most distant known planets, Uranus and Neptune, 
shows not the slightest variation from the law of Newton. 
But, owing to the rapid diminution with the distance to which 
the law of the inverse square gives rise when we take d Stances 
so immense as those which separate us from the fixed stars, 
the gravitation even of the sun is so small that a million 
years would be required for it to produce any important ef- 
fect. We are thus led to the law of universal gravitation, ex- 
pressed as follows : 

Every particle of matter in the universe attracts every oilier par- 
ticle with a force directly as their masses, and inversely as the 
square of the distance which sejiarates them. 

§ 2. Gravitation of Small Masses. — Density of the Earth. 

To make perfect the proof that gravity does really reside 
in each particle of matter, it was desirable to show, by actual 
experiment, that isolated masses did really attract each other, 
as required by Newton's law. This experiment has been 



82 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

made in various ways with entire success, the object, howev- 
er, being not to prove the existence of the attraction, but to 
measure the mean density of the earth, which admits of be- 
ing thus determined. The attraction of a sphere upon a point 
at its surface is shown, mathematically, to be the same as if 
the entire mass of the sphere were concentrated in its centre. 
It is, therefore, directly as the total amount of matter in the 
sphere, that is, its weight, and inversely as the square of its 
radius. Let us, then, compare the attraction of two spheres of 
the same material, of which the diameter of the one is double 
that of the other. The larger will have eight times the bulk, 
and therefore eight times the mass, of the smaller. But 
against this is the disadvantage that a particle on its surface 
is twice as far from its centre as in the case of the smaller 
sphere, which causes a diminution of one -fourth. Conse- 
quently, it will attract such a particle with double the force 
that the smaller sphere will ; that is, the attractions are direct- 
ly as the diameters of the spheres, if the densities are equal. 
If the densities are not equal, the attraction is proportional to 
the product of the density into the diameter. 

The diameter of the earth is, in round numbers, forty millions 
of feet. Consequently, the attraction of a sphere of the same 
mean density as the earth, but one foot in diameter, will be 
t o-oinroiro P ai,t the attraction of the earth ; that is, 40 ao TreRf^ 
the weight of the body attracted. Consequently, if we should 
measure the attraction of such a sphere of lead, and find that 
it was just 40 ooo ooo tnat °f tne weight of the body attracted, 
we would conclude that the mean density of the earth was 
equal to that of lead. But the attraction is actually found 
to be nearly twice as great as this ; consequently, a leaden 
sphere is nearly twice as dense as the average of the mat- 
ter composing the earth. Such a determination of the density 
of the earth is known as the Cavendish experiment, from the 
name of the physicist who first executed it. 

The method in which a task seemingly so hopeless as meas- 
uring a minute force like this is accomplished is shown in the 
following figures. It consists primarily of a torsion balance ; 



GRAVITATION OF SMALL MASSES. 






that is, a very light rod, <?, with a weight at each end, suspend- 
ed horizontally by a fine fibre of silk. In order to protect it 
against currents of air, it must be completely enclosed in a 
case. In Fig. 22, the balance eb is suspended from the end 




Fig. 22.— Baily's apparatus for determining the density of the earth hy the Cavendish ex- 
periment The left-hand ball b is hidden behind the weight W. 

of the arm KF by the fine fibre of silk, FK The weights to 
be attracted are at the two ends, bb. When thus suspend- 
ed, the balance will swing round in a horizontal direction, 
twisting the silk fibre, by a very small force. The attracting 
masses consist of a pair of leaden balls, WW, as large as the 
experimenter can procure and manage, which are supported 
on the turn-table, T. Jn Fig. 23, a view of the apparatus from 
above is given, showing the relative positions of the leaden 
balls, and the suspended weights which they are to attract. 
It will be seen that in the position in which the weights are 
represented in the figure their attraction tends to make the 
torsion balance turn in the direction opposite that of the hands 
of a watch. The effect of placing the leaden balls in this posi- 
tion is, that the balance begins to turn as described, and, being 
carried by its momentum beyond the position of equilibrium, 
at length comes to rest by the twisting of the silk thread by 
which it is suspended, and then is carried part of the way 



84 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 



back to its original position. It makes several vibrations, 
each requiring some minutes, and at length comes to rest in a 
position different from its original one. The attracting balls 
are then placed in the reverse position, corresponding to the 




>-, J'' 

Fig. 23.— View of Baily's apparatus from above. 

dotted lines, so that they tend to make the balance swing in 
the opposite direction, and the motions of the balance are 
again determined. These motions are noted by a small mi- 
croscope, viewed through the enclosure in which the whole 
apparatus is placed, and from these motions tlie attractions of 
the balls can be computed. 

Since this experiment was first made by Cavendish, it has 
been repeated by several other physicists; first by Professor 
Reich, of Freiberg, in 1838, and again by Francis Baily, Esq., 
of London. The latter repetition forms one of the most elab- 
orate and exhaustive series of experiments ever made ; we 
have therefore chosen Baily's apparatus for the purpose of 
illustration. The results for the mean density of the earth 
obtained by these several experiments are : 

Cavendish (his own result) 5.48 

" (Hutton's revision) 5.32 

Reich 5.44 

Baily 5.66* 

* Memoirs of the Royal Astronomical Society, vol. xix. 




DENSITY OF THE EARTH. 85 

The same problem has been attacked by attempting to de- 
termine the attraction of mountains, or portions of the crust 
of the earth. In fact, the first attempt 
of the sort ever made was by Maske- 
lyne, Astronomer Royal of England 
from 1766 to 1811, who determined 
the attraction of the mountain Sche- 
hallien, in Scotland, by observing its 
effect on the plumb-line. The princi- 
ple of this is very clear : on whichever 
side of a steep isolated mountain we 
hang a plumb-line, the attraction of F10.24. 

the mountain will cause it to incline towards it, the direction 
of gravity, or the apparent vertical, being changed from A B 
(Fig. 24) to AE, and from CD to CG. The density of the 
earth thus obtained was 4.71, a quantity much smaller than 
that afterwards given by the leaden balls. But this method 
is necessarily extremely uncertain, owing to the fact that the 
earth immediately beneath the mountain will probably not be 
of the same density as at a distance from it, and it is impos- 
sible to determine and allow for this difference. 

A third method is to determine the diminution of gravity 
as we descend into the earth. We have said that the attrac- 
tion of the earth upon a point outside of it is the same as if 
the whole mass of the earth were concentrated in its centre. 
Hence, as we rise above the surface of the earth, thus receding 
from the centre, the force of gravity diminishes. If this force 
all resided in the centre of the earth, it would continue to in- 
crease as we go below the surface. But such is not the case, 
because, once inside the earth, we have matter round and 
above us the attraction of which tends to lessen the gravity 
towards the centre. If we could actually reach the centre, 
the attraction would be nothing, because a point there would 
be equally attracted in every direction. If the density of the 
earth were uniform, the force of gravity would diminish with 
perfect uniformity from the surface to the centre. If the den- 
sity increases as we approach the centre, the diminution of 



86 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

gravity will be less rapid.* A determination of the density of 
the earth by the diminution of gravity in a mine was made 
by Professor Airy, at the Harton Colliery, in Wales, in 1855. 
His result was 6.56. This method is subject to uncertainty, 
from the difficulty of determining the density of that portion 
of the earth the attraction of which causes the gravity of bodies 
in the bottom of the mine to be diminished. 

§ 3. Figure of the Earth. 

If the earth did not revolve, the mutual attraction of all its 
parts would tend to make it assume a spherical form. If the 
cohesion of the solid parts prevented the spherical form from 
being accurately assumed, nevertheless the surface of the 
ocean, or of any fluid covering the earth, would assume that 
form. If, now, we set such a spherical earth in rotation 
around an axis, a centrifugal force will be generated towards 
the equatorial regions, which will cause the ocean to move 
from the poles towards the equator, so that the surface will 
tend to assume the form of an oblate spheroid, the longest di- 
ameter passing through the equator, and the shortest through 
the poles. A computation of the centrifugal force at the 
equator shows it to be ^-g- the force of gravity itself. Conse- 
quently, the oblateness ought to be easily measurable in geo- 
detic operations. Yet another result was that, in consequence 
of the centrifugal force at the equator, bodies would be light- 
er, and a clock regulated to northern latitudes would lose 
time when taken thither. 

This last result accorded with the experience of Richer, 
sent by the French Academy to Cayenne, in 1672, to make ob- 
servations on Mars. After that, to deny the oblate figure of 
the earth was not so much to deny Newton's theory of gravity 

* The general law which regulates the force of gravity within the earth is this : 
The total attraction of the shell of earth, which is outside the attracted point ex- 
tending all around the glohe, is nothing, while the remainder of the globe, being 
a sphere with the point on its surface, attracts as if it were all concentrated at 
the centre. But this presupposes that the whole earth is composed of spherical 
layers, each of uniform density, which is not strictly the case. 



FIGURE OF THE EARTH. ST 

as to deny that mechanical forces produced their natural effect 
in changing the form of the surface of the ocean. Neverthe- 
less, the French astronomers long refused their assent, because 
the geodetic operations they had undertaken in France seemed 
to indicate that the earth was elongated rather than flattened 
in the direction of the poles. The real cause of this result 
was, that the distance measured in France was so short that 
the effect of the earth's ellipticity was entirely masked by the 
unavoidable errors of the measures, vet it long delayed the en- 
tire acceptance of the Newtonian theory by the French astron- 
omers. We must, however, give the latter, or, speaking of 
them individually, their successors of the next generation, the 
credit of taking the most thorough measures to settle the ques- 
tion. Their government sent one expedition to Peru, to meas- 
ure the length of a degree of latitude at the equator, and an- 
other to Lapland, to measure one as near as possible to the 
pole. The result was entirely in accord with the theory of 
Newton, and gave it a confirmation which had in the mean 
time become entirely unnecessary. 

Newton was unable to determine the exact figure which the 
earth ought to assume under the influence of its own attrac- 
tion and the centrifugal force of rotation, though he could see 
that its meridian lines would be curves not very different from 
an ellipse. The complication of the problem arises from the 
fact that, as the earth changes its form in consequence of the 
rotation, the direction and force of attraction at the various 
points of its surface change also; and this, in its turn, leads 
to a different figure. It was not until the middle of the last 
century that the problem of the form of a rotating fluid mass 
was solved, and the answer found to be an ellipsoid. 

The figure of the earth is, however, not an exact ellipsoid, 
there being two causes of deviation. (When we speak of the 
figure or dimensions of the earth, we mean those of the ocean 
as they would be if the ocean covered the entire earth.) One 
cause of deviation is that the density of the earth increases 
as we approach its centre. The other cause is that there are 
great irregularities in the density of its superficial portions. 



88 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

In consequence of this, the real figure of the water-line is Ml 
of small deviations, which are rendered very evident by the 
refined determinations of modern times, and which are very 
troublesome to all who are engaged in exact geodetic opera- 
tions. 

§ 4. Precession of the Equinoxes. 

Yet another mysterious phenomenon which gravity com- 
pletely explained was that of the precession of the equinoxes. 
We have already described this as a slow change in the posi- 
tion of the pole of the celestial sphere among the stars, lead- 
ing to a corresponding change in the position of the celestial 
equator. But the Copernican theory shows the celestial pole 
to be purely fictitious, because the heavens do not revolve at 
all, but the earth. The pole of the celestial sphere is only 
that point of the heavens towards which the axis of the earth 
points. Hence, when we come to the Copernican system, we 
see that precession must be in the earth, and not in the heav- 
ens, and must consist simply in a change in the direction of 
the earth's axis, in virtue of which it describes a circle in the 
heavens in about 25,800 years. This effect was traced by 
Newton to the attraction of the sun and moon on the protu- 
berance produced, as just described, by the centrifugal force 
at the earth's equator. In the present case the effect is much 
the same as if the earth, being itself spherical, were enveloped 
by a huge ring extending round its equator. In Fig. 25 let 



"CJ 



Fig. 25. 



AB represent this ring revolving around the sun, S ; the cen- 
trifugal force at its centre, c, will then balance the attraction of 
the sun at the same point. But the point A being nearer the 
sun, his attraction will be greater than at c, and the centrifu- 



PRECESSION OF THE EQUINOXES. 89 

gal force will be less, so that there will be a surplus force 
pulling A towards the sun. At B, on the other hand, the at- 
tractive force of the sun is less, and the centrifugal force is 
greater. Consequently, there is a surplus force tending to 
draw B from the sun. The ring being oblique towards the 
sun, the effect of these surplus forces would be to make the 
ring turn round at c until the line AB pointed towards the 
sun. The spherical earth being fastened in the ring, as just 
supposed, would very slowly be turned round with the ring, so 
that its equator would be directed towards the sun. But this 
effect is prevented by the earth's rotation on its axis, which 
makes it act like a gyroscope, or like a spinning-top. Instead 
of being brought down towards the sun, a very slow motion, at 
right angles to this direction, is produced, and thus we have 
the motion of precession. The nature of this motion may be 
best seen by Fig. 17, where the north pole of the earth is rep- 
resented as constantly inclined to the right of the observer as 
the earth moves round the sun, so that the solstices are at A 
and C, and the equinoxes at B and D. The effect of the at- 
traction of the sun and moon on the protuberance at the 
equator is, that in 6500 years the axis of the earth will incline 
towards the observer of the picture, with nearly the inclina- 
tion of 23° ; so that the solstices will be at B and D, and the 
equinoxes at A and C. In 6500 years more the north pole 
will be pointed towards the left instead of the right, as in the 
figure; in 6500 more it will be directed from the observer: 
and, finally, at the end of a fourth period it will be once more 
near its present position. 

The effects we have described would not occur if the plane 
of the ring, AB, passed through the sun, because then the 
forces which draw A towards the sun and B from it, would act 
directly against each other, and so destroy each other's effect. 
Kow, this is the case twice a year, namely, when the sun is on 
the equator. Therefore, the motion of precession is not uni- 
form, but is much greater than the average in June and De- 
cember, when the sun's declination is greatest ; and is less in 
March and September, when the sun is on the plane of the 



90 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

equator. Moreover, in December the earth is nearer the sun 
than in June, aud the force greater, so that we have still an- 
other inequality from this cause. 

Precession is not produced by the sun alone. The moon is 
a yet more powerful agent in producing it, its smaller mass 
being more than compensated by its greater proximity to ns.* 
The same causes which make the action of the sun variable 
make that of the moon variable also, and we have the addi- 
tional cause that, owing to the revolution of the moon's node, 
the inclination of the moon's orbit to the plane of the earth's 
equator is subject to an oscillation having a period of 18.6 
years, producing an inequality of this same period in the pre- 
cession. The several inequalities in the precession which we 
have described are known as nutation of the earth's axis, and 
are all accurately computed and laid down in astronomical 
tables. 

§ 5. The Tides. 

It has been known to seafaring nations from a remote an- 
tiquity that there was a singular connection between the ebb 
and flow of the tides, and the diurnal motion of the moon. 
Csesar's description of his passages across the English Channel 
shows that he was acquainted with the lawr In describing 
the motion of the moon, it was shown that, owing to her revo- 
lution in a monthly orbit, she rises, passes the meridian, and 
sets about fifty minutes later every day. The tides ebb and 
flow twice a day, but the corresponding tide is always later 
than the day before, by the same amount, on the average, that 
the moon is later. Hence, at any one place, the tides always 
occur when the moon is near the same point of her apparent 
diurnal course. 



* This may need some explanation, as the attractive force of the sun upon the 
earth is more than a hundred times that of the moon. The force which produces 
precession is proportional to the difference of the attractions on the two sides of 
the earth, or on A and B in Fig. 25, and this difference is greater in the case of 
the moon's attraction. In fact, it varies inversely as the cube of the distance of 
the attracting body. 



THE TIDES. 91 

The cause of this ebb and flow of the sea, and its relation 
to the moon, was a mystery until gravitation showed it to be 
due to the attraction of the moon on the waters of the ocean. 
The reason why there are two tides a day will appear by 
studying the case of the moon's revolution around the earth. 
Let M be the moon, E the earth, and EM the line joining their 
centres. Now, strictly speaking, the moon does not revolve 
around the earth, any more than the earth around the moon ; 
but, by the principle of action and reaction, both move around 
their common centre of gravity. The earth being eighty 
times as heavy as the moon, this centre is situated within the 
former, about three-fourths of the way from its centre to its 
surface, at the point G in the figure. The manner in which 

B 




Q 



\jy 



A 

Fig. 26.— Attraction of the moon tending to produce tides. 

the moon produces the tides is much the same as that in 
which precession is produced. Near the centre of the earth, 
A 7 , the centrifugal force of the earth's monthly rotation around 
G, and the attraction of the moon, counterbalance each other, 
so that a point there has no disposition to move under the influ- 
ence of these combined forces. As we pass from E to D, the 
part of the earth's surface opposite the moon, the centrifugal 
force around G keeps increasing, owing to onr greater distance 
from the centre, while the attraction of the moon diminishes. 
Hence, at D the centrifugal force predominates, and tends to 
throw the waters of the ocean out, as shown in the figure. 
Again, as we pass from the centre E to C, the centrifugal force 
constantly diminishes till we reach the centre of revolution, 
G, when it vanishes, and, beyond 67, begins to act in the oppo- 
site direction. Hence, at C the attraction of the moon and 
the small centrifugal force around G both combine to throw 



92 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

the waters of the ocean out in the direction of the moon. 
Thus, there is a force causing the waters to rise at D and (7, 
and therefore to fall at A and B ; and there are, therefore, two 
tides to each apparent diurnal revolution of the moon. 

If the waters everywhere yielded immediately to the at- 
tractive force of the moon, it would always be high -water 
when the moon was on the meridian, low-water when she was 
rising or setting, and high-water again when she was in the 
middle of that portion of her course which is under the hori- 
zon. But, owing to the inertia of the water, some time is 
necessary for so slight a force to set it in motion, and, once in 
motion, it continues so after the force has ceased, and until it 
has acted some time in the opposite direction. Therefore, if 
the motion of the water were unimpeded, it would not be 
high- water until some hours after the moon had passed the 
meridian. Yet another circumstance interferes with the free 
motion of the water — namely, the islands and continents. 
These deflect the tidal wave from its course in such a way that 
it may, in some cases, be many hours behind its time, or even 
a whole day. Sometimes two waves may meet each other, 
and raise an extraordinarily high tide. At other times the 
tides may have to run up a long bay, where the motion of a 
long mass of water will cause ah enormous tide to be raised. 
In the Bay of Fundy both of these causes are combined. A 
tidal wave coming up the Atlantic coast meets the ocean 
wave from the east, and, entering the bay with their com- 
bined force, the water at the head of it is forced up to the 
height of sixty or seventy feet, on the principle seen in the 
hydraulic ram. 

The snn produces a tide as well as the moon, the force 
which it exerts on the two sides of the earth being the same, 
which, acting on the equatorial protuberance of the earth, 
produces precession. The tide-producing force of the sun is 
about -fa of that of the moon. At new and full moon the two 
bodies unite their forces, and the result is that the ebb and 
flow are greater than the average, and we have the " spring- 
tides." When the moon is in her first or third quarter, the 






INEQUALITIES IN THE MOTIONS OF THE PLANETS. 93- 

two forces act against each other ; the tide-producing force is 
the difference of the two, the ebb and flow are less than the 
average, and we have the " neap-tides." 

§ 6. Inequalities in the Motions of the Planets produced by their 
Mutual Attraction. 

The profoundest question growing out of the theory of 
gravitation is whether all the inequalities in the motion of the 
moon and planets admit of being calculated from their mut- 
ual attraction. This question can be completely answered 
only by actually making the calculation, and seeing whether 
the resulting motion of each planet agrees exactly with that 
observed. The problem of computing the motion of each 
planet under the influence of the attraction of all the other- 
is, however, one of such complexity that no complete and per- 
fect solution has ever been found. Stated in its most general 
form, it is as follows: Any number of planets of which the 
masses are known are projected into space, their positions, ve- 
locities, and directions of motion all being given at some one 
moment. They are then left to their mutual attractions, ac- 
cording to the law of gravitation. It is required to And gen- 
eral algebraic formula? by which their position at any time 
whatever shall be determined. In this general form, no ap- 
proximation to an entire solution has ever been found. But 
the orbits described by the planets around the sun, and by the 
satellites around their primaries, are nearly circular; and this 
circumstance affords the means of computing the theoretical 
place of the planet as accurately as we please, provided the 
necessary labor can be bestowed upon the work. 

What makes the problem so complex is that the forces 
which act upon the planets are dependent on their motions, 
and these again are determined by the forces which act on 
them. If the planets did not attract each other at all, the 
problem could be perfectly solved, because they would then 
all move in ellipses, in exact accordance with Kepler's laws. 
Supposing them to move in ellipses, their positions and dis- 
tances at any time could be expressed in algebraic formula?, 



94 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

and their attractions on each other could be expressed in the 
same way. But, owing to these very attractions, they do not 
move in ellipses, and therefore the formulae thus found will 
not be strictly correct. To put the difficulty into a nut-shell, 
the geometer cannot strictly determine the motion of the plan- 
et until he knows the attractions of all the other planets on it, 
and he cannot determine these without first knowing the posi- 
tion of the planet, that is, without having solved his problem. 

The question how to surmount these difficulties has, to a 
greater or less extent, occupied the attention of all great math- 
ematicians from the time of Newton till now; and although 
complete success has not attended their efforts, yet the mar- 
vellous accuracy with which sun, moon, and planets move in 
their prescribed orbits, and the certainty with which the laws 
of variation of those orbits through countless ages past and to 
come have been laid down, show that their labor has not been 
in vain. Newton could attack the problem only in a geomet- 
rical way ; he laid down diagrams, and showed in what way 
the forces acted in various parts of the orbits of the two plan- 
ets, or in various positions of the sun and moon. He was thus 
enabled to show how the attraction of the sun upon the moon 
changes the orbit of the latter around the earth, and causes its 
nodes to revolve from east to west, as observations had shown 
them to do, and to calculate roughly one or two of the inequal- 
ities in the motion of the moon in her orbit. 

When the Continental mathematicians were fully convinced 
of the correctness of Newton's theory, they immediate^ at- 
tacked the problem of planetary motion with an energy and 
talent which placed them ahead of \\\e rest of the world. 
They saw the entire insufficiency of Newton's geometrical 
method, and the necessity of having the forces which moved 
the planets expressed by the algebraic method, and, by adopt- 
ing this system, were enabled to go far ahead both of New- 
ton and his countrymen. The last half of the last century 
was the Golden Age of mathematical astronomy. Five il- 
lustrious names of this period outshine all others: Clairaut, 
D'Alembert, Euler, Lagrange, and Laplace, all, except Euler, 






INEQUALITIES IN THE MOTIONS OF THE PLANETS. 95 

French by birth or adoption. The great works which closed 
it were the " Mecanique Celeste " of Laplace, and the " M6- 
canique Analytique" of Lagrange, which embody the sub- 
stance of all that was then known of the subject, and form the 
basis of nearly everything that has since been achieved. We 
shall briefly mention some of the results of these works, aiid 
those of their successors which may interest the Don - mathe- 
matical reader. 

Perhaps the most striking of these results is that of the sec- 
ular variations of the planetary orbits. Copernicus and Kep- 
ler had found, by comparing tbe planetary orbits as observed 
by themselves with those of Ptolemy, that the forms and posi- 
tions of those orbits were subject to a slow change from cen- 
tury to century. The immediate successors of Newton were 
able to trace this change to the mutual action of the planets, 
and thus arose the important question, Will it continue fur- 
ever? For, should it do so, it would end in the ultimate sub- 
version of the solar system, and the destruction of all life on 
our globe. The orbit of the earth, as well as of the other plan- 
ets, would become so eccentric that, approaching near the sun at 
one time, and receding far from it at another, the vicissitudes 
of temperature would be insupportable. Lagrange, however, 
was enabled to show by a mathematical demonstration that 
these changes were due to a regular system of oscillations ex- 
tending throughout the whole planetary system, the periods of 
which were so immensely long that only a progressive motion 
could be perceived during all the time that men had observed 
the planets. The number of these combined oscillations is 
equal to that of the planets, and their periods range from 
50,000 years all the way up to 2,000,000— " Great clocks of 
eternity, which beat ages as ours beat seconds." In conse- 
quence of these oscillations, the perihelia of the planets will 
turn in every direction, and the orbits will vary in eccentricity, 
but will never become so eccentric as to disturb the regularity 
of the system. About 18,000 years ago, the eccentricity of the 
earth's orbit was about .019 ; it has been diminishing ever 
since, and will continue to diminish for 25,000 years to come, 

8 



96 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

when it will be more nearly a circle than any orbit of onr sys- 
tem now is. 

Some of the questions growing out of the moon's motion 
are not completely settled yet. Early in the last century it 
was found by Halley, from a comparison of ancient eclipses 
with modern observations of the moon, that oiir satellite was 
accelerating her motion around- the earth. She was, in fact, 
about a degree ahead of where she ought to have been had 
her motion been uniform from the time of Hipparchus and 
Ptolemy. The existence of this acceleration was fully estab- 
lished in the time of Lagrange and Laplace, and was to them 
a source of great perplexity, because they had conceived them- 
selves to have shown mathematically that the mutual attrac- 
tions of the planets or satellites could never accelerate or re- 
tard their mean motions in their orbits, and thus the motion 
of the moon seemed to be affected by some other force than 
gravitation. After several vain attempts to account for the 
motion, it was found by Laplace that, in consequence of the 
secular diminution of the eccentricity of the earth's orbit, the 
action of the sun on the moon was progressively changing in 
such a manner as to accelerate its motion. Computing the 
amount of the acceleration, he found it to be about 10 sec- 
onds in a century, and its action on the moon being like that 
of gravity on a falling body, the total effect would increase as 
the square of the time ; that is, while in one century the moon 
would be 10 seconds ahead, in two centuries she would be 40 
seconds ahead, in three centuries 90 seconds, and so on. 

This result agreed so well with the observed acceleration, 
as determined by a comparison of ancient eclipses with mod- 
ern data, that no one doubted its correctness till long after the 
time of Laplace. But, in 1853, Mr. J. C. Adams, of England, 
celebrated as one of the two mathematicians who had calcu- 
lated the position of Neptune from the motions of Uranus, un- 
dertook to recompute the effect of the variation of the earth's 
eccentricity on the mean motion of the moon. He was sur- 
prised to find that, carrying his process farther than Laplace 
had done, the effect in question was reduced from 10 seconds, 



INEQUALITIES IN THE MOTION OF THE MOON. 97 

the result of Laplace, to 6 seconds. On the other hand, the 
farther examination of ancient and modern observations 
seemed to show that the acceleration as given by them wag 
even greater than that found by Laplace, being more nearly 
12 seconds than 10 seconds ; that is, it was twice as great as 
that computed by Mr. Adams from the theory of gravitation. 
• The announcement of this result by Mr. Adams was at first 
received with surprise and incredulity, and led to one of the 
most remarkable of scientific discussions. Three of the great 
astronomical mathematicians of the day — Hansen, Plana, and 
De Pontecoulant — disputed the correctness of Mr. Adams's 
result, and maintained that that of Laplace was not affected 
with any such error as Mr. Adams had found. In fact, Hansen, 
by a method entirely different from that of his predecessors, 
had found a result of 12 seconds, which was yet larger than 
that of Laplace. On the other hand, De&unay, of Paris, by a 
new and ingenious method of his own, found a result agreeing 
exactly with Mr. Adams's. Thus, the five leading experts of 
the day were divided into two parties on a purely mathemat- 
ical question, and several years were required to settle the dis- 
pute. The majority had on their side not only the facts of 
observation, so far as they went, but the authority of Laplace: 
and, if the question could have been settled either by observa- 
tion or by authority, they must have carried the day. But the 
problem was altogether one of pure mathematics, depending 
on the computation of the effect which the gravitation of the 
sun ought to produce on the motion of the moon. Both par- 
ties were agreed as to the data, and but one correct result was 
possible, so that an ultimate decision could be reached only by 
calculation. 

The decision of such a question could not long be delayed. 
There was really no agreement among the majority as to what 
the supposed error of Mr. Adams consisted in, or what the ex- 
act mathematical expression for the moon's acceleration was. 
On the other hand, Mr. Adams showed conclusively that the 
methods of De Pontecoulant and Plana were fallacious; and the 
more profoundly the question was examined, the more evident 



98 SYSTEM OF TEE WOULD HISTORICALLY DEVELOPED. 

it became that he was right. Mr. Cayley made a computation 
of the result by a new method, and Delaunay by yet another 
method, and both agreed with Mr. Adams's. Although their 
antagonists never formally surrendered, they tacitly abandon- 
ed the field, leaving Delaunay and Adams in its undisturbed 
possession.* 

It was thus conclusively settled that the true value of the 
acceleration was about 6", the last value found by Delaunay 
being 6".18. This result was only about half of that which 
had been derived from the observations of ancient eclipses, so 
that there appeared to be a discrepancy between the observed 
and the theoretical acceleration, the cause of which was to 
be investigated. A possible cause happened to be already 
known : the friction of the tidal wave must constantly retard 
the diurnal motion of the earth on its axis, though it is impos- 
sible to say how mufch this retardation may amount to. The 
consequence would be that the day would gradually, but un- 
ceasingly, increase in length, and our count of time, depend- 
ing on the day, would be always getting too slow. The moon 
would, therefore, appear to be going faster, when really it was 
only the earth which was moving more slowly. So long as 
theory had agreed with the observed acceleration of the moon, 
there had been no need to invoke this cause ; but, now that 
there was a difference, it afforded the most plausible explana- 
tion. 

Thus the theory of the subject is that there is an undoubted 
real acceleration of 6".18, and an additional apparent accel- 
eration of a few seconds, due to the tidal retardation of the 
earth's rotation, the amount of which can be found only by 
comparing the motions of the moon in different centuries. 
The absence of precise observations in ancient times renders 
this determination difficult and' uncertain. The ancient rec- 
ords which have been most relied on are the narratives of sup- 

* The writer has reason to believe it an historical fact that Hansen, on revising 
his own calculations, and including terms he at first supposed to be insensible, 
found that he would be led substantially to the result of Adams, although he 
never made any formal publication of this fact. 



INEQUALITIES IN THE MOTION OF TEE MOON 99 

posed total eclipses of the sun, which have been handed down 
to us by the Greek and Roman classical writers. The most 
ancient and celebrated of these eclipses is associated with the 
name of Thales, the Ionian philosopher, our knowledge of 
which is derived from the following account by Herodotus : 

" Now after this (for Alyattes did not by any means sur- 
render the Scythians at the demand of Cyaxares) there was 
war between the Lydians and the Medes for the space of five 
years, in which [period] the Medes often conquered the Lydi- 
ans, and the Lydians, in turn, the Medes. And, in this time, 
they also had a night engagement; for as they were protract- 
ing the war with equal success on each side, in a battle that 
occurred in the sixth year, it happened, as the armies en- 
gaged, that the day was suddenly turned into night. Now 
this change of the day [into night] Thales, the Milesian, had 
predicted to the Ionians, placing as the limit of the period 
[within which it would take place] this very year in which 
it did actually occur. Now, both the Lydians and the Medes, 
when they saw night coming on instead of day, ceased from 
battle, and both parties were more eager to make peace with 
each other." 

If, in this case, we knew when and where the battle was 
fought, and if we knew that the darkness referred to was 
really that of a total eclipse of the sun, it would be easy to 
compute very nearly what must have been the course of the 
moon in order that the dark shadow might have passed over 
the field of battle. But, to the reader who reflects upon the 
uncritical character of Herodotus, the vagueness of his descrip- 
tion of the occurrence will suggest some suspicions whether 
we have really a total eclipse to deal with. Besides, the time 
when the battle was fought is doubtful by twenty years or 
more, and the only way in which it has been fixed is by cal- 
culating from the tables of the sun and moon all the total 
eclipses which passed over the region in which the battle took 
place between the admissible limits of time. Thus, it is found 
that the only date which will fulfil the conditions is May 28th, 
b.c. 584, when there must have been a total eclipse in Asia 



100 SYSTEM OF THE WOULD HISTORICALLY DEVELOPED. 

Minor or its neighborhood. But, unless we suppose that it 
was really a total eclipse which caused the battle to cease, 
nothing can be concluded respecting it; and as this point 
seems uncertain, it is not likely that astronomers will lay 
much stress upon it. 

Another celebrated eclipse of the sun is known as the 
eclipse of Agathocles. The fleet of this commander, being 
blockaded in the port of Syracuse by the Carthaginians, was 
enabled to escape to sea at a moment when the attention of 
the enemy was diverted by a provision convoy, and sailed to 
make a descent upon Carthage. " The next day there was 
such an eclipse of the sun that the day wholly put on the 
appearance of night, stars being seen everywhere." There is 
no reasonable doubt that this was a total eclipse of the sun, 
and the date is well established, being August 14th, b.c. 309. 
But, unfortunately, it is not known whether Agathocles went 
to the north or the south of Sicily in his passage to Car- 
thage, and hence we cannot obtain any certain result from 
this eclipse. 

These historical accounts of total eclipses being uncertain, 
an attempt has been made to derive the moon's acceleration 
from the eclipses of the moon recorded by Ptolemy in the 
Almagest, and from the observations of the Arabian astrono- 
mers in the ninth and tenth centuries. These observations 
agree as fairly as could be expected in assigning to the moon 
a secular acceleration of about 8".4, a little more than 2" 
greater than that computed from gravitation. On the other 
hand, if we accept the eclipse of Thales as total where the 
battle was fought,' the total acceleration will be about 12". so 
that the two results are entirely incompatible. The question 
which is correct must be decided by future investigation; but 
the author believes the smaller value to be founded on the 
more trustworthy data. 

The secular acceleration is not the only variation in the 
moon's mean motion which has perplexed the mathematicians. 
About the close of the last century, it was found by Laplace 
that the moon had, for a number of years, been falling behind 



INEQUALITIES IN THE MOTION OF THE MOON. 101 

her calculated place, a result which seemed to show that there 
was some oscillation of long period which had been overlooked. 
He made two conjectural explanations of this inequality, but 
both were disproved by subsequent investigators. The ques- 
tion, therefore, remained without any satisfactory solution till 
1846, when Hansen announced that the attraction of Venus 
produced two inequalities of long period in the moon's mo- 
tion, which had been previously overlooked, and that these 
fully accounted for the observed deviations of the moon's po- 
sition. These terms were recomputed by Delaunay, and he 
found for one of them a result agreeinc: very well with Han- 
sen's. But the second came out so small that it could never be 
detected from observations, so that here was another mathe- 
matical discrepancy. There was not room, however, for much 
discussion this time. Hansen himself admitted that he had 
been unable to determine the amount of this inequality in a 
satisfactory manner from the theory of gravitation, and had 
therefore made it agree with observation, an empirical process 
which a mathematician would never adopt if he could avoid 
it. Even if observations were thus satisfied, doubt would still 
remain. But it has lately been found that this empirical 
term of Hansen's no longer agrees with observation, and that 
it does not satisfactorily agree with observations before 1700. 
In consequence, there are still slow changes in the motion of 
our satellite which gravitation has not yet accounted for. We 
are, apparently, forced to the conclusion either that the motion 
of the moon is influenced by some other cause than the gravi- 
tation of the other heavenly bodies, or that these inequalities 
are only apparent, being really due to small changes in the 
earth's axial rotation, and in the consequent length of the day. 
If we admit the latter explanation, it will follow that the 
earth's rotation is influenced by some other cause than the 
tidal friction; and that, instead of decreasing uniformly, it va- 
ries from time to time in an irregular manner. The observed 
inequalities in the motion of the moon may be fully accounted 
for by changes in the earth's rotation, amounting in the ag- 
gregate to half a minute or so of time — changes which could 



102 SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

be detected by a perfect clock kept going for a number of 
years. But, as it takes many years for these changes to occur, 
no clock yet made will detect them. 

Yet another change not entirely accounted for on the the- 
ory of gravitation occurs in the motion of the planet Mercury. 
From a discussion of all the observed transits of this planet 
across the disk of the sun, Leverrier has found that the mo- 
tion of the perihelion of Mercury is about 40 seconds in a 
century greater than that computed from the gravitation of 
the other planets. This he attributes to the action of a group 
of small planets between Mercury and the sun. In this form, 
however, the explanation is not entirely satisfactory. In the 
iirst place, it seems hardly possible that such a group of plan- 
ets could exist without being detected during total eclipses of 
the sun, if not at other times. In the next place, granting 
them to exist, they must produce a secular variation in the 
position of the orbit of Mercury, whereas this variation seems 
to agree exactly with theory. Leverrier explains this by sup- 
posing the group of asteroids to be in the same plane with the 
orbit of Mercury, but it is exceedingly improbable that such 
a group would be found in this plane. There is, however, an 
allied explanation which is at least worthy of consideration. 
The phenomenon of the zodiacal light, to be described here- 
after, shows that there is an immense disk of matter of some 
kind surrounding the sun, and extending out to the orbit of 
the earth, where it gradually fades away. The nature of this 
matter is entirely unknown, but it may consist of a swarm of 
minute particles, revolving round the sun, and reflecting its 
light, like planets. If the total mass of these particles is equal 
to that of a very small planet, say a tenth the mass of the 
earth, it would cause the observed motion of the perihelion of 
Mercury. The evidence on this subject will be considered 
more fully in treating of Mercury. 

With the exceptions just described, all the motions in the 
solar system, so far as known, agree perfectly with the results 
of the theory of gravitation. The little imperfections which 
still exist in the astronomical tables seem to proceed mainly 



RELATION OF THE PLANETS AND STARS. 103 

from errors in the data from which the mathematician must 
start in computing the motion of any planet. The time of 
revolution of a planet, the eccentricity of its orbit, the position 
of its perihelion, and its place in the orbit at a given time, can 
none of them be computed from the theory of gravitation, but 
must be derived from observations alone. If the observations 
were absolutely perfect, results of any degree of accuracy 
could be obtained from them; but the imperfections of all 
instruments, and even of the human sight itself, prevent ob- 
servations from attaining the degree of precision sought after 
by the theoretical astronomer, and make the considerations of 
"errors of observation" as well as of "errors of the tables" 
constantly necessary. 

§ 7. Relation of the Planets to the Stars. 

In Chapter L, § 3, it was stated that the heavenly bodies 
belong to two classes, the one comprising a vast multitude of 
stars, which always preserved their relative positions, as if they 
were set in a sphere of crystal, while the others moved, each 
in its own orbit, according to laws which have been described. 
We now know that these moving bodies, or planets, form a 
sort of family by themselves, known as the Solar Sy6tem. 
This system consists of the sun as its centre, with a number of 
primary planets revolving around it, and satellites, or second- 
ary planets, revolving around them. Before the invention of 
the telescope but six primary planets were known, including 
the earth, and one satellite, the moon. By the aid of that in- 
strument, two great primary planets, outside the orbit of Sat- 
urn, and an immense swarm of smaller ones between the or- 
bits of Mars and Jupiter, have been discovered ; while the 
four outer planets — Jupiter, Saturn, Uranus, and Neptune — 
are each the centre of motion of one or more satellites. The 
sun is distinguished from the planets, not only by his immense 
mass, which is several hundred times that of all the other bod- 
ies of his system combined, but by the fact that he shines by 
his own light, while the planets and satellites are dark bodies, 
shining only b} T reflecting the light of the sun. 



104: SYSTEM OF THE WORLD HISTORICALLY DEVELOPED. 

A remarkable symmetry of structure is seen in this system, 
in that all the large planets and all the satellites revolve in 
orbits which are nearly circular, and, the satellites of the two 
outer planets excepted, nearly in the same plane. This family 
of planets are all bound together, and kept each in its respec- 
tive orbit, by the law of gravitation, the action of which is of 
such a nature that each planet may make countless revolutions 
without the structure of the system undergoing any change. 

Turning our attention from this system to the thousands of 
fixed stars which stud the heavens, the first thing to be consid- 
ered is their enormous distance asunder, compared with the 
dimensions of the solar system, though the latter are them- 
selves inconceivably great. To give an idea of the relative 
distances, suppose a voyager through the celestial spaces could 
travel from the sun to the outermost planet of our system in 
twenty-four hours. So enormous would be his velocity, that it 
would carry him across the Atlantic Ocean, from New York 
to Liverpool, in less than a tenth of a second of the clock. 
Starting from the sun with this velocity, he would cross the 
orbits of the inner planets in rapid succession, and the outer 
ones more slowly, until, at the end of a single day, he would 
reach the confines of our system, crossing the orbit of Neptune. 
But, though he passed eight planets the first day, he would 
pass none the next, for he would have to journey eighteen or 
twenty years, without diminution of speed, before he would 
reach the nearest star, and would then have to continue his 
journey as far again before he could reach another. All the 
planets of our system would have vanished in the distance, in 
the course of the first three days, and the sun would be but an 
insignificant star in the firmament. The conclusion is, that 
our sun is one of an enormous number of self-luminous bodies 
scattered at such distances that years would be required to 
traverse the space between them, even when the voyager went 
at the rate we have supposed. The solar and the stellar sys- 
tems thus offer us two distinct fields of inquiry, into which we 
shall enter after describing the instruments and methods by 
which they are investigated. 



PART IL— PRACTICAL ASTRONOMY. 



INTRODUCTORY REMxVJlKS. 

Should the reader ask what Practical Astronomy is, the 
best answer might be given him by a statement of one of its 
operations, showing how eminently practical our science is. 
"Place an astronomer on board a ship; blindfold him : carry 
him by any route to any ocean on the globe, whether under 
the tropics or in one of the frigid zones ; land him on the 
wildest rock that can be found; remove his bandage, and give 
him a chronometer regulated to Greenwich or Washington 
time, a transit instrument with the proper appliances, and the 
necessary books and tables, and in a single clear night he can 
tell his position within a hundred yards by observations of the 
stars." This, from a utilitarian point of view, is one of the 
most important operations of Practical Astronomy. When we 
travel into regions little known, whether on the ocean or on 
the Western plains, or when we wish to make a map of a 
country, we have no way of finding our position by reference 
to terrestrial objects. Our only course is to observe the heav- 
ens, and find in what point the zenith of our place intersects 
the celestial sphere at some moment of Greenwich or Wash- 
ington time, and then the problem is at once solved. The in- 
struments and methods by which this is done may also be ap- 
plied to celestial measurements, and thus we have the art and 
science of Practical Astronomy. To speak more generally, 
Practical Astronomy consists in the description and investiga- 
tion of the instruments and methods employed by astronomers 
in the work of exploring and measuring the heavens, and of 



106 PRACTICAL ASTRONOMY. 

determining positions on the earth by observations of the heav- 
enly bodies. The general construction of these instruments, 
and the leading principles which underlie their use and em- 
ployment, can be explained with the aid of a few technical 
terms which we shall define as we have occasion for them. 

The instruments employed by the ancients in celestial ob- 
servations were so few and simple that we may dispose of 
them very briefly. The only ones we need mention at pres- 
ent are the gnomon and the astrolabe, or armillary sphere. 
The former was little more than a large sun-dial of the sim- 
plest construction, by which the altitude and position of the 
sun were determined from the length and direction of the 
shadow of an upright pillar. If the sun were a point to the 
sight, this method would admit of considerable accuracy, be- 
cause the shadow would then be sharply defined. In fact, 
however, owing to the apparent size of the solar disk, the shad- 
ow of any object at the distance of a few feet becomes ill-de- 
fined, shading off so gradually that it is hard to say where it 
ends. No approach to accuracy can therefore be attained by 
the gnomon. 

Notwithstanding the rudeness of this instrument, it seems 
to have been the one universally employed by the ancients 
for the determination of the times when the sun reached 
the equinoxes and solstices. The day when the shadow was 
shortest marked the summer solstice, and a comparison of 
the length of the shadow with the height of the style gave, 
by a trigonometric calculation, the altitude of the sun. The 
day when the shadow was longest marked the winter solstice ; 
and the day when the altitude of the sun was midway between 
the altitudes at the two solstices marked the equinoxes. Thus 
this rude instrument served the purpose of determining the 
length of the year with an accuracy sufficient for the purposes 
of daily life. But so immensely superior are our modern 
methods in accuracy, that the astronomer can to-day compute 
the position of the sun at any hour of any day 2000 years ago 
with far greater accuracy than it could have been observed 
with a gnomon. 



INTRODUCTORY REMARKS. 



107 



The armillary sphere consisted of a combination of three 
circles, one of which could be set in the plane of the equator 
or the ecliptic; that is, an arm moving around this circle 
would always point towards some part of the equator or the 
ecliptic, according to the way the instrument was set. The 
circle in question, being divided into degrees, served the pur- 
pose of measuring the angular distance of any two bodies in 
or near the ecliptic, as the sun and moon, or a star and planet. 
It was by such measures that Hipparchus and Ptolemy were 
able to determine the larger inequalities in the motions of the 
sun, moon, and planets. 



E A 




Fig. 2T.— Armillary sphere, as described by Ptolemy, and used by him and by Hipparchus. 
The circle EI is set in the plane of the ecliptic, the line PP being directed towards its 
pole. The circle ApMp passes through the poles of both the ecliptic and the equator. 
The inner pair of circles turn on the axis PP, and are furnished with sights which may 
be directed on the object to be observed. The latitude and longitude of the object are 
then read off by the position of the circles. 



108 PRACTICAL ASTRONOMY. 



CHAPTER I. 

THE TELESCOPE. 

§ 1. The First Telescopes. 

The telescope is so essential a part of every instrument in- 
tended for astronomical measurement, that, apart from its own 
importance, it must claim the first place in any description of 
astronomical instruments. The question, Who made the first 
telescope ? was long discussed, and, perhaps, will never be con- 
clusively settled. If the question were merely, Who is entitled 
to the credit of the invention under the rules according to 
which scientific credit is now awarded ? we conceive that the 
answer must be, Galileo. The first publisher of a result or 
discovery, supposing such result or discovery to be honestly 
his own, now takes the place of the first inventor ; and there 
is little doubt that Galileo was the first one to show the w T orld 
how to make a telescope. But Galileo himself says that it 
was through hearing that some one in France or Holland had 
made an instrument which magnified distant objects, and 
brought them nearer to the view, that he was led to inquire 
how such a result could be reached. He seems to have ob- 
tained from others the idea that the instrument was possible, 
but no hint as to how it w T as made. 

As a historic fact, however, there is no serious question that 
the telescope originated in Holland ; but the desire of the in- 
ventors, or of the authorities, or both, to profit by the posses- 
sion of an instrument of such extraordinary powers, prevented 
the knowledge of its construction from spreading abroad. The 
honor of being the originator has been claimed for three men, 
each of whom has had his partisans. Their names are Metius, 



THE FIRST TELESCOPES. 109 

Lipperhey, and Jansen ; the last two being spectacle-makers 
in the town of Middleburg, and the first a professor of mathe- 
matics. 

The claims of Jansen were sustained by Peter Borelli, au- 
thor of a small book* on the subject, and on the strength of 
his authority Jansen was long held to be the true inventor. 
His story was that Jansen had shown a telescope sixteen inches 
long to Prince Maurice and the Archduke Albert, who, per- 
ceiving the importance of the invention in war, offered him 
money to keep it a secret. If this story be true, it would be 
interesting to know on what terms Jansen was induced to sell 
out his right to immortality. But Borelli's case rests od the 
testimony of two or three old men who had known Jansen in 
their youth, taken forty-five or fifty years after the occurrence 
of the events, when Jansen had long been dead, and has there- 
fore never been considered as fully proved. 

About 1830, documentary evidence was discovered which 
showed that Hans Lipperhey, whom Borelli claims to have 
been a second inventor of the telescope, made application to 
the States-general of Holland, on November 2d, 1608, for a 
patent for an instrument to see with at a distance. About 
the same time a similar application was made by James Me- 
tins. The Government refused a patent to Lipperhey, on the 
ground that the invention was already known elsewhere, but 
ordered several instruments from him, and enjoined him to 
keep their construction a secret. # 

It will be seen from this that the historic question, Who 
made the first telescope? does not admit of being easily an- 
swered ; but that the powers of the instrument were well 
known in Holland in 1608 seems to be shown by the refusal 
of a patent to Lipperhey. The efforts made in that country 
to keep the knowledge of the construction a secret were so 
far successful that w r e must go from Holland to Italy to find 
how that knowledge first became public property. About six 
months after the petitions of Lipperhey and Metius, Galileo 

* *"l)e Vero Telescopii Inventore,"' The Hague, 1655. 



HO PRACTICAL ASTRONOMY. 

was in Venice on a visit, and there received a letter from 
Paris, in which the invention was mentioned. He at once set 
himself to the reinvention of the instrument, and was so suc- 
cessful that in a few days he exhibited a telescope magnify- 
ing three times, to the astonished authorities of the city. Re- 
turning to his home in Florence, he made other and larger 
ones, which revealed to him the spots on the sun, the phases 
of Venus, the mountains on the moon, the satellites of Jupiter, 
the seeming handles of Saturn, and some of the myriads of 
stars, separately invisible to the naked eye, whose combined 
light forms the milky-way. But the largest of these instru- 
ments magnified only about thirty times, and was so imper- 
fect in construction as to be far from showing as much as 
could be seen with a modern telescope of that power. The 
Galilean telescope was, in fact, of the simplest construction, 
consisting of the combination of a pair of lenses, of which the 
larger was convex and the smaller concave, as shown in the 
following figure : 



Fig. 28.— The Galilean telescope. The dotted lines show the course of the rays through 

the lenses. 

The distance of the lenses was such that the rays of light 
from a star passing through the large convex lens, or object- 
glass, OB, met the concave lens, B, before reaching the focus. 
The position of this concave lens was such that the rays 
should emerge from it nearly parallel. This form of tele- 
scope is still used in opera -glasses, because it can be made 
shorter than any other. 

The improvements in the telescope since Galileo can be 
best understood if we give a brief statement of the princi- 
ples on which all modern telescopes are constructed. The 
properties of every such instrument depend on the power pos- 
sessed by a lens or by a concave mirror of forming an im- 
age of any distant object in its focus. This is done in the 



THE FIRST TELESCOPES. HI 

case of the lens by refracting the light which passes through 
it, and in the case of the mirror by reflecting back the rays 
which strike it. In order to form an image of a point, it is 
necessary that a portion of the rays of light which emanate 
from the point shall be collected and made to converge to 
some other point. For instance, in the following figure, the 



-- — i 



Fig. 29.— Formation of an image by a lens. 

nearly parallel rays emanating from a distant point in the di- 
rection from which the arrow is coming strike the lens, L. 
and as they pass through it are bent out of their course, and 
made to converge to a point, F. Continuing their course, 
they diverge from F exactly as if F itself were a luminous pointy 
a cone of light being formed with its apex at F. An observer 
placing his eye within this cone of rays, and looking at F, 
will there seem to see a shining point, although really there 
is nothing there. This apparent shining point is, in the lan- 
guage of astronomy, called the image of the real point. The dis- 
tance, OF, is called the focal length of the lens. 

If, instead of a simple point, we have an object of some 
apparent magnitude, as the moon, a house, or a tree, then the 
light from each point of the object will be brought to a cor- 
responding point near F. To find where this corresponding 
point is, we have only to draw a line from each point of an 
object through the centre of the lens, and continue it as far as 
the focus. Each point of the object will then have its own 
point in the image. These points, or images, will be spread 
out over the surface, EFE. which is called the focal plane, and 
will make up a representation, or image, of the entire object 
on a small scale, but in a reversed position, exactly as in the 
camera of a photographer. An eye at B within the cone of 
rays will then see all or a part of the object reversed in the 
focal plane. The image thus formed mav be viewed bv the 

9 



112 PRACTICAL ASTRONOMY. 

eye as if it were a real object; and as a minute object may be 
viewed by a magnifying lens, so such a lens may be used to 
view and magnify the image formed in the focal plane. In 
the large lens of long focus to form the image in the focal 
plane, and the small lens to view and. magnify this image, we 
have the two essential parts of a refracting telescope. The 
former lens is called the objective, or object-glass, and the latter 
the eye-piece, eye-lens, or ocular. 

The magnifying power of a telescope depends upon the rel- 
ative focal lengths of the objective and ocular. The greater 
the focal length of the former — that is, the greater the distance 
OF — the larger the image will be ; and the less the focal length 
of the eye-lens, the nearer the eye can be brought to the im- 
age, and the more the latter will be magnified. The magnify- 
ing power is found by dividing the focal length of the objec- 
tive by that of the eye-lens. For instance, if the focal length 
of an objective were 36 inches, and that of the eye-lens were 
three-quarters of an inch, the quotient of these numbers would 
be 48, which would be the magnifying power. If the focal 
lengths of these lenses were equal, the telescope would not 
magnify at all. By simply turning a telescope end for end, 
and looking in at the objective, we have a reversed telescope, 
which diminishes objects in the same proportion that it mag- 
nifies them when not reversed. 

From the foregoing rule it follows that we can, theoretical- 
ly, make any telescope magnify as much as we please, by sim- 
ply using a sufficiently small eye -lens. If , for instance, we 
wish our telescope of 36 inches focal length to magnify 3600 
times, we have only to apply to it an eye-lens of yj^ of an inch 
focal length. But, in attempting to do this, a difficulty arises 
with which astronomers have always had to contend, and 
which has its origin in the imperfection of the image formed 
by the object -glass. No lens will bring all the rays of light 
to ' absolutely the same focus. When light passes through a 
prism, the various colors are refracted unequally, red being 
refracted the least, and violet the most. It is the same 
when light is refracted by a lens; and the consequence is that 



THE FIRST TELESCOPES. 115 

the red rays will be brought to the farthest focus, and the vio- 
let to the nearest, while the intermediate colors will be scat- 
tered between. As all the light is not brought to the same 
focus, it is impossible to get any accurate image of a star or 
other object at which the telescope is pointed, the eye seeing 
only a confused mixture of images of various colors. When 
a sufficiently low magnifying power is used, the confusion will 
be slight, the edges of the object being indistinct, and made 
up of colored fringes. When the magnifying power is in- 
creased, the object will indeed look larger, but these confused 
fringes will look larger in the same proportion ; so that the 
observer will see no more than before. This separation of the 
light in a telescope is termed chromatic aberration. 

Such was the difficulty which the successors of Galileo en- 
countered in attempting to improve the telescope, and which 
they found it impossible to obviate. They found, however, 
that they could diminish it by increasing the length of the tel- 
escope, and the consequent size of the confused image. If 
they made an object-glass of any fixed diameter, say six inches, 
they found that the image was no more confused when the 
focal length was sixty feet than when it was six, and the same 
eye-lens could therefore be used in both cases. But the im- 
age in the focus of the first was ten times as large as in the 
second, and thus using the same eye-lens would give ten times 
the magnifying power. Huyghens, Cassini, Hevelius, and oth- 
er astronomers of the latter part of the seventeenth century, 
made telescopes a hundred feet or upwards in length. Some- 
astronomers then had to dispense with a tube entirely ; the ob- 
jective being mounted by Cassini on the top of a long pole, 
while the ocular was moved along near the ground. Hevelius 
kept his objective and ocular connected by a long rod which 
replaced the tube. Very complicated and ingenious arrange- 
ments were sometimes used in managing these huge instru- 
ments, of which we give one specimen, taken from the work 
of Blanchini, "Hesperi et Phosphori Nova Phenomena" in which 
that astronomer describes his celebrated observations on the 
rotation of Venus. 



110 PRACTICAL ASTRONOMY. 

§ 2. The Achromatic Telescope. 

A century and a half elapsed from the time when Galileo 
showed his first telescope to the authorities of Venice before 
any method of destroying the chromatic aberration of a lens 
was discovered. It is to Dollond, an English optician, that the 
practical construction of the achromatic telescope is due, al- 
though the principle on which it depends was first published 
by Euler, the German mathematician. The invention of Dol- 
lond consists in the combination of a convex and concave lens 
of two kinds of glass in such a way that their aberrations 
shall counteract each other. How this is effected will be best 
seen by taking the case of refraction by a prism, where the 
same principle comes into play. The separation of the light 
into its prismatic colors is here termed dispersion. Suppose, 
now, that we take two prisms of glass, ABC and A CD, (Fig. 
31), and join them in the manner shown in the figure. If a 



n- 




B C 

Fig. 31.— -Kefraction through a compound prism. 

my, US, pass through the two, their actions on it will tend 
to counteract each other, owing to the opposite directions in 
which their angles are turned, and the ray will be refracted 
only by the difference of the refractive powers, and dispersed 
by the difference of the dispersive powers. If the dispersive 
powers are equal, there will be no dispersion at. all, the ray 
passing through without any separation of its colors. If the 
two prisms are made of the same kind of glass, their dispersive 
powers can be made equal only by making them of the same 
angle, and then their refractive powers will be equal also, and 
the ray will pass through without any refraction. As our ob- 



THE ACHROMATIC TELESCOPE. 117 

ject is to have refraction without dispersion, a combination of 
prisms of the same kind of glass cannot effect it. 

The problem which is now presented to us is, Can we make 
two prisms of different kinds of glass such that their disper- 
sive powers shall be equal, but their refractive powers un- 
equal? The researches of Euler and Dollond answered this 
question in the affirmative by showing that the dispersive 
power of dense flint-glass is double that of crown-glass, while 
its refractive power is nearly the same. Consequently, if we 
make the prism ABC of crown glass, and the prism ACD of 
flint, the angle of the flint at being half that of the crown 
at A, the two opposite dispersions will neutralize each other, 
and the rays will pass through without being broken up into 
the separate colors. But the crown prism, with double the an- 
gle, will have a more powerful refractive power than the flint ; 
so that, by combining the two, we shall have refraction without 
dispersion, which solves the problem. 

The manner in which this principle is applied to the con- 
struction of an object-glass is this : a convex lens of crown is 
combined with a concave lens of flint of about half the cur- 
vature. No exact rule respecting the ratio of the two curva- 
tures can be given, because the refractive powers of different 
specimens of glass differ greatly, and the proper ratio must, 
therefore, be found by trial in each case. Having found it. 
the two lenses will then have equal aberrations, but in oppo- 
site directions, while the crown refracting more powerfullv 
than the flint, the rays will be brought to a focus at a dis- 
tance a little more than double the focal distance of the former. 
A combination of this sort is called an achromatic objective. 
Some of the earlier achromatic objectives were made of three 
lenses, a double concave lens of flint glass being fitted be- 
tween two double convex ones of crown. At present, how- 
ever, but two lenses are used, the forms of 

which, as used in the smaller European tele- f — -, 

scopes, and in all the telescopes of Mr. Alvan l=^^^^I^J 
Clark, are shown in Fi^. 32. The crown- Crown 

... Tii i t i Fig. 32.— Section of an 

glass is here a double convex lens, and the achromatic objective. 



118 PRACTICAL ASTRONOMY. 

curvatures of the two faces are equal. The curvature of the 
inside face of the flint is the same as that of the crown, so 
that the two faces fit accurately together, while the outer face 
is nearly flat. If the dispersive power of the flint were just 
double that of the crown, this face would have to be flat 
to produce achromatism ; but this is not generally the case. 
The fact is that, as no two specimens of glass made at dif- 
ferent meltings have exactly the same refractive and disper- 
sive powers, the optician, in making a telescope, must find the 
ratios of dispersion of his two glasses, and then give the outer 
face of his flint such a degree of curvature as to neutralize 
the dispersion of his crown glass. Usually, this face will have 
to be slightly concave. 

When the inner faces of the glasses are thus made to fit, it 
is not uncommon to join the glasses together with a transpar- 
ent balsam, in order to diminish the loss of light in passing 
through the glass. Whenever light falls upon transparent 
glass, between three and four per cent, of it is reflected back, 
and when, after passing through, it leaves again, about the 
same amount is reflected back into the glass. Consequently, 
about seven per cent, of the light is lost in passing through 
each lens. But when the two lenses are joined with balsam 
or castor-oil, the reflection from the second surface of the flint 
and the first surface of the crown is greatly diminished, and a 
loss of perhaps six per cent, of the light is avoided.* 

As larger and more perfect achromatic telescopes were 
made, a new source of aberration was discovered, no practical 
method of correcting which is yet known. It arises from the 
fact that flint glass, as compared with crown, disperses the blue 
end of the spectrum more than the red end. If we make 



* When there is no balsam, another inconvenience sometimes arises from a 
double reflection of light from the inner surfaces of the glass. Of the light re- 
flected back from the first surface of the crown, four per cent, is again reflected 
from the second surface of the flint, and sent down to the focus of the telescope 
with the direct rays. If there be the slightest misplacement of one of the lenses, 
the reflected rays will come to a different focus from the direct ones, and every 
bright star will seem to have a small companion star along-side of it. 






THE ACHROMATIC TELESCOPE. 119 

lenses of flint and crown having equal dispersive power, we 
shall find that the red end is longest in the crown-glass spec- 
trum, and the blue end in the flint-glass spectrum. The con- 
sequence is that when w r e join a pair of prisms in reversed 
positions, as shown in Fig. 31, the two dispersions cannot be 
made to destroy each other entirely. Instead of the refracted 
light being all joined in one white ray, the spectrum will be 
folded over, as it were, the red and indigo ends being joined 
together, the faint violet light extending out by itself, while 
the yellow and green are joined at the opposite end. This 
end will, therefore, be of a yellowish green, while the other 
end is purple. 

The spectrum thus formed by the combination of a flint 
and crown prism is termed the secondary spectrum. It is very 
much shorter than the ordinary spectra formed by either the 
crown or the flint glass, and a large portion of the light is con- 
densed near the yellowish-green end. The effect of it is that 
the refracting telescope is not perfectly achromatic, though 
very nearly so. In a small telescope the defect is hardly no- 
ticeable, the only drawback being that a bright star or other 
object is seen surrounded by a blue or violet areole, formed by 
the indigo rays thrown out by the flint-glass. If the eye-piece 
is pushed in, so that the star is seen, not as a point, but as a 
small disk, the centre of this disk will be green or yellow, 
while the border will be reddish purple. But, in the immense 
refractors of two-feet aperture or upwards, of which a number 
have been produced of late years, the secondary aberration 
constitutes the most serious optical defect ; and it is a defect 
which, arising from the properties of glass itself, no art can 
diminish. The difficulty may be lessened in the same way 
that the chromatic aberration was lessened in the older tele- 
scopes, namely, by increasing the length of the instrument. 
In doing this, however, with glasses of such large size, engi- 
neering difficulties are encountered which soon become insur- 
mountable. We must, therefore, consider that, in the great 
refractors of recent times, the limit of optical power for such 
instruments has been very nearly attained. 



120 PRACTICAL ASTRONOMY. 

The eye-piece of a telescope, as well as its objective, con- 
sists of two glasses. A single lens will, indeed, answer all 
the purposes of seeing an object in the centre of the field 
of view, but the field itself will be narrow and indistinct at 
the edges. An additional lens, term- 
ed the field -lens, is therefore placed 
very near the image, for the purpose 



\ E * jj of refracting the outer rays into the 

proper direction to form a distinct 
image with the aid of the eye -lens. 
^ \tZ2&r*~ I" Kg- 33 such an eye-piece is rep- 
resented, in which the field -lens is 
between the image and the eye. This is called a positive 
eye-piece. In the negative eye-piece the rays pass through 
the field-lens just before coming to a focus, so that the image 
is formed just within that lens. The positive eye -piece is 
used when it is required to use a micrometer in the focal 
plane ; but for mere looking the negative ocular is best. All 
telescopes are supplied with a number of eye -pieces, by 
changing which the magnifying power may be altered to suit 
the observer. 

The astronomical telescope used with these eye-pieces al- 
ways shows objects upside down and right side left. This 
causes no inconvenience in celestial observations. But for 
viewing terrestrial objects the eye-piece must have two pairs 
of lenses, the first of which forms a new image of the object 
restored to its proper position, which image is viewed by the 
eye -piece formed of the second pair. This combination is 
called an erecting or terrestrial eye-piece. 

§ 3. The Mounting of the Telescope. 

If the earth did not revolve, so that each heavenly body 
would be seen hour after hour and day after day in nearly 
the same direction, the problem of using great telescopes 
would be much simplified. The objective and the eye-piece 
could be fixed so as to point at the object, and the observer 
could scrutinize it at his leisure. But actually, when we use 



THE MOUNTING OF THE TELESCOPE. 121 

a telescope, the diurnal revolution of the earth is apparently 
increased in proportion to the magnifying power of the in- 
strument; and if the latter is fixed, and a high power is used, 
the object passes by with such rapidity that it is impossible to 
scrutinize it. Merely to point a telescope at an object needs 
many special contrivances, because, unless the pointing is ac- 
curate, the object cannot be found at all. With a telescope, 
and nothing more, an observer might spend half an hour in 
vain efforts to point it at Sirius so accurately that the image 
of the star should be brought into the field of view; and then, 
before he got one good look, it might flit away and be lost 
again. If this is the case with a bright star, how much harder 
must it be to point at the planet Neptune, an object invisible 
to the naked eye, which is not in the same direction two min- 
utes in succession! It will readily be understood that, to make 
any astronomical use of a large telescope, two things are abso- 
lutely necessary: first, the means of pointing the telescope at 
any object, visible or invisible; and, second, the means of mov- 
ing the telescope so that 
it shall follow the object 
in its diurnal motion, 
and thus keep its image 
in the field of view. The 
following are the me- 
chanical contrivances by / An 

which these objects are 
effected: jp \\ -, \\r 

The object-glass is ^ I l/ V_ i 

placed in one end of a A — — ; — I — = — 

tube, OF, the length of / j — ! — j r 

the tube being nearly 
equal to the focal length 

of the objective. The 

eye-piece is fitted into a 
projection at the lower 
end of the tube, E. The 

• . « -j , . Fig. 34.— Mode of mounting a telescope so as to fol- 

Ohject OI tne tube IS tO low a star in its diurnal motion. 




122 PRACTICAL ASTRONOMY. 

keep the glasses in their proper relative positions, and to pro- 
tect the eye of the observer from stray light. 

The tube has an axis, AB, firmly fastened to it at A near its 
middle, which axis passes through a cylindrical case, C, into 
which it neatly fits, and in which it can turn. By turning the 
telescope on this axis, the end E can be brought towards the 
reader, and from him, or vice versa. This axis is called the 
declination axis. The case, (7, is firmly fastened to a second 
axis, BE, supported at D and E called the polar axis. This 
axis points to the pole of the heavens, and, by turning it, the 
whole telescope, with the part, A C, of the case, may be brought 
towards the observer, while the end B will recede from him, 
or vice versa. In order that the weight of the telescope may 
not make it turn on the polar axis, it is balanced by a weight 
at B, on the other end of the declination axis. This weight 
is commonly divided, a part being carried by the axis, and a 
part by the case, C. The polar axis is carried by a frame, F, 
well fastened on top of a pier of masonry. 

Such is the general nature of the mechanism by which an 
astronomical telescope is mounted. The essential point is 
that there shall be two axes — one fixed, and pointing at the 
pole, and one at right angles to it, and turning with it. In 
the arrangement of these axes there are great differences in 
the telescopes of different makers ; but Fig. 34 shows what 
is essential in the plan of mounting now very generally 
adopted. 

In the figure the telescope is represented as east of the spec- 
tator, and as pointed at the pole, and therefore parallel to the 
polar axis. Suppose now that the telescope be turned on the 
declination axis, AB, through an arc of 90°, the eye-piece, E, 
being brought towards the spectator ; the object end will then 
point towards the east horizon, and therefore towards the celes- 
tial equator, the eye end pointing directly towards the spec- 
tator. Then let the whole instrument be turned on the polar 
axis, the eye-piece being brought downwards. The telescope 
will then move along the celestial equator, or the path of a 
star, 90° from the pole. And at whatever distance from the 



THE REFLECTING TELESCOPE. 123 

pole we set it by turning it on the declination axis, if we 
turn it on the polar axis it will describe a circle having the 
pole at its centre ; that is, the same circle which a star follows 
by its diurnal motion. So, to observe a star with the telescope, 
we have first to turn it on the declination axis to the polar dis- 
tance of the star, and then oh the polar axis till it points at 
the star. This pointing is effected by circles divided into de- 
grees and minutes, not shown in the figure, by which the dis- 
tance which the telescope points from the pole and from the 
meridian may be found at any time. 

In order that the star, when once found, may be kept in the 
field of view, the telescope is furnished with a system of clock- 
work, by which the polar axis is slowly turned at the rate of 
one revolution a day. By starting this clock-work, the tele- 
scope is made to follow the star in its diurnal motion ; or. t< i 
speak with greater astronomical precision, as the earth turns 
on its axis from west to east, the telescope turns from east t'» 
west with the same angular velocity, so that the direction in 
which it points in the heavens remains unaltered. 

In order to facilitate the finding or recognition of an object, 
the telescope is furnished with a " finder," T^ consisting of a 
small telescope of low power pointing in the same direction 
with the larger one. An object can be seen in the small tel- 
escope without the pointing being so accurate as is necessary 
in the case of the large one ; and, when once seen, the tele- 
scope is moved until the object is in the middle of the field 
of view, when it is also in the field of view of the large one. 

§ 4. The Reflecting Telescope. 

Two radically different kinds of telescopes are made : the 
one just described, known as the refracting telescope, because 
dependent on the refraction of light through glass lenses ; and 
the other, the reflecting telescope, so called because it acts by 
reflecting the light from a concave mirror. The name of the 
first inventor of this instrument is disputed; but Sir Isaac 
Newton was among the first to introduce it. It was designed 
by him to avoid the difficulty growing out of the chromatic 



124 PRACTICAL ASTRONOMY. 

aberration of the refracting telescopes of his time, which, it 
will be remembered, were not achromatic. If parallel rays of 
light from a distant object fall upon a concave mirror, as shown 
in Fig. 35, they will all be reflected back to a focus, F, half- 
way between the centre of curvature, (7, and the surface of 



J2 



Fig. 35. — Speculum bringing rays to a single focus by reflection. 

the mirror. In order that the rays may be all reflected to 
absolutely the same focus, the section of the mirror must be 
a parabola, and the point where the rays meet will be the 
focus of the parabola. If the rays emanate from the various 
points of an object, an image of this object will be formed 
in and near the focus, as in the case of a lens. This image 
is to be viewed with a magnifying eye-piece like that of a 
refracting telescope. Such a mirror is called a speculum. 

Here, however, a difficulty arises. The image is formed on 
the same side of the mirror on which the object lies; and in or- 
der that it may be seen directly, the eye of the observer and 
the eye-piece must be between F and G, directly in the rays 
of light emanating from the object. By placing the eye here, 
not only would a great deal of the light be cut off by the body 
of the observer, but the definition of the image would be great- 
ly injured by the interposition of so large an object. Three 
plans have been devised for evading this difficulty, which are 
due, respectively, to Gregory, Newton, and Herschel. 

The Herschelian Telescope. — In this form of telescope the 
mirror is slightly tipped, so that the image, instead of being 
formed in the centre of the tube, is formed near one side of 
it, as in Fig. 36. The observer can then view it without put- 
ting his head inside the tube, and, therefore, without cutting 
off any material portion of the light. In observation, he must 
stand at the upper, or outer, end of the tube, and look into it, 
his back being turned towards the object. From his looking 



THE REFLECTING TELESCOPE. 



125 



directly into the mirror, it was also called the "front-view" 
telescope. The great disadvantage of this arrangement is that 




Fig. 36.— Herschelian telescope. 

the rays cannot be brought to an exact focus when they are 
thrown so far to one side of the axis, and the injury to the 
definition is so great that the front-view plan is now entirely 
abandoned. 

The Newtonian Telescopte. — The plan proposed by Sir Isaac 
Newton was to place a small plane mirror just inside the fo- 
cus, inclined to the telescope at an angle of 45°, so as to throw 
the rays to the side of the tube, where they come to a focus, 
and form the image. An opening is made in the side of the 
tube, just below where the image is formed in which the eye- 
piece is inserted. This mirror cuts off some of the light, but 
not enough to be a serious defect. An improvement which 
lessens this defect has been made by Professor Henry Draper. 




Fig. 37 — Horizontal section of a Newtonian telescope. This section shows how the lumi- 
nous rays reflected from the parabolic mirror M meet a small rectangular prism m n. 
which replaces the inclined plane mirror used in the old form of Newtonian telescope. 
After undergoing a total reflection from m n, the rays form at a 6 a very small image 
of the heavenly body. 

The inclined mirror is replaced by a small rectangular prism, 
by reflection from which the image is formed very near the 
prism. A pair of lenses are then inserted in the course of 



126 



PRACTICAL ASTRONOMY. 



the rays, by which a second image is formed at the opening 
in the side of the tube, and this second image is viewed by 
an ordinary eye -piece. The four lenses together form an 
erecting eye-piece. 

The Gregorian Telescope. — This is a form proposed by James 
Gregory, who probably preceded Newton as an inventor of the 
reflecting telescope. Behind the focus, F, a small concave 
mirror, B, is placed, by which the light is reflected back again 




Fig. 38.— Section of the Gregorian telescope. 

down the tube. The larger mirror, if, has an opening through 
its centre, and the small mirror, B, is so adjusted as to form a 
second image of the object in this opening. This image is 
then viewed by an eye-piece which is screwed into the opening. 

The Cassegrainian Telescope — In principle the same with the 
Gregorian, differs from it only in that the small mirror, B, is 
convex, and is placed inside the focus, F, so that the rays are 
reflected from it before reaching the focus, and no image is 
formed until they reach the opening in the large mirror. 
This form has an advantage over the Gregorian in that the 
telescope may be made shorter, and the small mirror can be 
more easily shaped to the required figure. It has therefore 
entirely superseded the original Gregorian form. 

Optically, these forms of telescope are inferior to the New- 
tonian. But the latter is subject to the inconvenience that the 
observer must be stationed at the upper end of the telescope, 
where he looks into an eye-piece screwed into the side of the 
tube. If the telescope* is a small one, this inconvenience is 
not felt ; but with large telescopes, twenty feet long or up- 
wards, the case is entirely different. Means must then be pro- 
vided by which the observer may be carried in the air at a 
height equal to the length of the instrument, and this requires 
considerable mechanism, the management of which is often 



THE PRINCIPAL TELESCOPES OF MODERN TIMES. 127 

very troublesome. On the other hand, the Cassegrainian tele- 
scope is pointed directly at the object to be viewed, like a re- 
fractor, and the observer stands at the lower end, and looks in 
at the opening through the large mirror. This is. therefore, 
the most convenient form of all in management. One draw- 
back is, that there are two mirrors to be looked after, and, un- 
less the figure of both is perfect, the image will be distorted. 
Another is the great size of the image, which forces the ob- 
server to use either a high magnifying power, or an eye-piece 
of corresponding size.* But these defects are of little impor- 
tance compared with the great advantage of convenient use. 

§ 5. The Principal Great Reflecting Telescopes of Moder 

The reflecting telescopes made by Newton and his contem- 
poraries were very small indeed, none being more than a few 
inches in diameter. Though vastlv more manageable than the 
immensely long refractors of Iluyghens, they do not seem to 
have exceeded them in effectiveness. We might, therefore, 
have expected the achromatic telescope to supersede the re- 
flector entirely, if it could be made of large size. But in the 
time of Dollond it was impossible to produce disks of flint-glass 
of sufficient uniformity for a telescope more than a very few 
inches in diameter. An achromatic of four inches aperture 
was then considered of extraordinary size, and good ones of 
more than two or three inches were rare. Consequently, for 
the purpose of seeing the most faint and difficult objects, the 
earlier achromatics were little, if any, better than the long 
telescopes of Iluyghens and Cassini. As there were no such 
obstacles to the polishing of large mirrors, it was clear that it 
was to the reflecting telescope that recourse must be had for 
any great increase in optical power. Before the middle of 
the last century the reflectors were little larger than the re- 
fractors, and had not exceeded them in their optical perform- 
ance. But a genius now arose who was to make a wonderful 
improvement in their construction. 



* The Melbourne telescope has an eve-lens six inches in diameter. 

10* 



128 PRACTICAL ASTRONOMY. 

William Herschel, in 1766, was a church-organist and teach- 
er of music of very high repute in Bath, who spent what little 
leisure he had in the study of mathematics, astronomy, and 
optics. By accident a Gregorian reflector two feet long fell 
into his hands, and, turning it to the heavens, he was so enrapt- 
ured with the views presented to him that he sent to London 
to see if he could not purchase one of greater power. The 
price named being far above his means, he resolved to make 
one for himself. After many experiments with metallic al- 
loys, to learn which would reflect most light, and many efforts 
to find the best way of polishing his mirror, and giving it a 
parabolic form, he produced a five-foot Newtonian reflector, 
which revealed to him a number of interesting celestial phe- 
nomena, though, of course, nothing that was not already known. 
Determined to aim at nothing less than the largest telescope 
that could be made, he attempted vast numbers of mirrors of 
constantly increasing size. The large majority of the individ- 
ual attempts were failures ; but among the results of the suc- 
cessful attempts were telescopes of constantly increasing size, 
until he attained the hitherto unthought-of aperture of two feet, 
with a length of twenty feet. With one of these he discov- 
ered the planet Uranus. The fame of the musician-astrono- 
mer reaching the ears of King George III., that monarch gave 
him a pension of £200 per annum, to enable him to devote 
his life to a career of astronomical discovery. He now made 
the greatest stride of all by completing a reflector four feet 
in diameter and forty feet long, with which he discovered two 
new satellites of Saturn. 

Herschel now found that he had attained the limit of man- 
ageable size. The observer had to be suspended perhaps thir- 
ty or forty feet in the air, in a room large enough to hold, not 
only himself, but all the means necessary for recording his 
observations ; and this room had to follow the telescope as it 
moved, to keep a star in the field. To this was added the 
difficulty of keeping the mirror in proper figure, the mere 
change of temperature in the night operating injuriously in 
this respect. We need not, therefore, be surprised to learn 



TEE PRINCIPAL TELESCOPES OF MODERN TIMES. 129 







Fig. 39.— Herschel's great telescope. 

• 

that Herschel made very little use of this instrument, and pre- 
ferred the twenty-foot even in scrutinizing the most difficult 
objects.* 

* Herschel's great instrument is still preserved, but is not mounted for use : 
indeed, it is probable that the minor lost all its lustre long years ago. In 1830. 
Sir John Herschel dismounted it, laid it in a horizontal position, and closed it up 
after a family celebration inside the tube, at which the following song was sung : 

THE OLD TELESCOPE. 

[To be sung on Xew-year's-eve, lS39-'40, b>i Papa. Mamma, Madame Gerlach, and all the Little 
Bodies in the Tube thereof assembled. J 

In the old Telescope's tube we sit, 
And the shades of the past around us flit ; 
His requiem sing we with shout and din, 
While the old year goes out, and the new comes in. 
Chorus. — Merrily, merrily let us all sing, 

And make the old telescope rattle and ring ! 



130 PRACTICAL ASTRONOMY. 

The only immediate successor of Sir William Herschel in 
the construction of great telescopes was his son, Sir John Her- 
schel. But the latter made none to equal the largest of his 
father's in size, and it is doubtful whether they exceeded them 
in optical power. 

The first decided advance on the great telescope was the 
celebrated reflector of the Earl of Rosse,* at Parsonstown, Ire- 



Ptill fifty years did he laugh at the storm, 
And the blast could not shake his majestic form ; 
Now prone he lies, where he once stood high, 
And searched the deep heaven with his broad, bright eye. 
Chorus.— Merrily, merrily, etc., etc. 

There are wonders no living sight has seen, 
Which within this hollow have pictured been ; 
Which mortal record can never recall, 
And are known to Him only who made them all. 
Chorus.— Merrily, merrily, etc., etc. 

Here watched our father the wintry night, 
And his gaze has been fed with preadamite light. 
His labors were lightened by sisterly love, 
And, united, they strained their vision above. 
Chorus.— Merrily, merrily, etc., etc. 

He has stretched him quietly down, at length, 
To bask in the starlight his giant strength ; 
And Time shall here a tough morsel find 
For his steel-devouring teeth to grind. 
. Chorus.— Merrily, merrily, etc., etc. 

He will grind it at last, as grind it he must, 
And its brass and its iron shall be clay and rust ; 
But scathless ages shall roll away, 
And nurture its frame, and its form's decay. 
Chorus. — Merrily, merrily, etc., etc. 

A new year dawns, and the old year's past ; 
God send it, a happy one like the last 
(A little more sun and a little less rain 
To save us from cough and rheumatic pain). 
Chorus. — Merrily, merrily, etc., etc. 

God grant that its end this group may find 
In love and in harmony fondly joined ! 
And that some of us, fifty years hence, once more 
May make the old Telescope's echoes roar. 
Chorus. — Merrily, merrily, etc., etc. 

* William Parsons, third Earl of Eosse, the original constructor of this tele- 
scope, died in 1867. The work of the instrument is continued by his son, the pres- 
ent earl. 



THE PRINCIPAL TELESCOPES' OF MODERN TIMES. 133 

land. The speculum of this telescope is six feet in diameter, 
and about fifty-four feet focal length, and was cast in 1842. 
One of the great improvements made by the Earl of Rosse 
was the introduction of steam machinery for grinding and 
polishing the great mirror, an instrumentality of which Her- 
schel could not avail himself. The mounting of this telescope 
is decidedly different from that adopted by Herschel. The 
telescope is placed between two walls of masonry, which only 
allow it to move about 10° on each side of the meridian, and 
it turns on a pivot at the lower end of the tube. It is moved 
north and south in the meridian by an ingenious combination 
of chains, and may thus be set at the polar distance of any 
star which it is required to observe. It is then moved slowly 
towards the west, so as to follow the star, by a long screw 
driven by an immense piece of clock-work. It is commonly 
used as a Newtonian, the observer looking into the side of the 
tube near the upper end. To enable him to reach the mouth 
of the tube, various systems of movable platforms and staging 
are employed. One of the platforms is suspended south of 
the piers ; it extends east and west by the distance between 
the walls, and may be raised by machinery so as to be directly 
under the mouth of the telescope so long as the altitude of the 
latter is less than 45°. When the altitude is greater than this, 
the observer ascends a stairway to the top of one of the walls, 
where he mounts one of several sliding stages, by which he 
can be carried to the mouth of the telescope, in any position 
of the latter. This instrument has been employed principal- 
ly in making drawings of lunar scenery and of the planets* 
and nebulae. Its great light-gathering power peculiarly tits it 
for the latter object. 

Other Reflecting Telescopes. — Although no other reflector ap- 
proaching the great one of the Earl of Rosse in size has ever 
been made, some others are worthy of notice, on account of 
their perfection of figure and the importance of the discov- 
eries made with them. Among these the first place is due to 
the great reflectors of Mr. William Lassell, of England. This 
gentleman made a reflector of two feet aperture about the 



134 



PRACTICAL ASTRONOMY. 



same time that Rosse constructed his immense six-foot. The 
perfection of figure of the mirror was evinced by the discov- 
ery of two satellites of Uranus, which had been previously un- 
known and unseen, unless, as is possible, Herschel and Struve 
caught glimpses of them on a few occasions. He afterwards 
made one of four feet aperture, which, in 1863, he took to the 
island of Malta, where he made a series of observations on 
satellites and nebulae. 




Fig. 41.— Mr. Lassell's great four-foot reflector, as mounted at Malta. 

In 1870, a reflecting telescope four feet in diameter, on the 
Cassegrainian plan, was made by Thomas Grubb & Son, of 
Dublin, for the Observatory of Melbourne, Australia. This 
instrument is remarkable, not only for its perfection of figure, 
but as being probably the most easily managed large reflector 
ever made. 




Fig. 42.— The new Paris reflector. 



THE PRINCIPAL TELESCOPES OF MO I) EPS TIMES. 137 

The only American who has ever successfully undertaken 
the construction of large reflecting telescopes is Professor Hen- 
ry Draper, of New York, who has one of twenty-eight inches 
aperture, the work of his own hands. This instrument was 
mounted about 1872 in the owner's private observatory at 
Hastings, on the Hudson. The mirror is not of speculum 
metal, but of silvered glass, and is almost perfect in figure. 
This telescope has been principally employed in making pho- 
tographs of celestial objects, and can be used either as ■ New- 
tonian or a Cassegrainian. 

An attempt has recently been made at the Paris Observa- 
tory to construct a reflecting telescope with a mirror of sil- 
vered glass, as large as the great specula of Lassell and the 
Melbourne Observatory. The diameter of the glass is 1l ; " 
centimetres, a fraction of an inch short of four English feet 
It was figured, polished, and silvered at the Paris Observa- 
tory by M. Martin, using the methods devised by Foucault. 
It was mounted in 1875; but, unfortunately, the proper meas- 
ures were not taken to prevent the glass from bending under 
its own weight, and thus destroying the perfection of the 
parabolic figure which M. Martin had succeeded in obtain- 
ing. It was therefore taken from its tube to have this defect 
of mounting remedied. The machinery for supporting and 
moving this telescope being in some respects peculiar, we pre- 
sent a view of it in Fig. 42, on page 134. 

§ 6. Great Refracting Telesco/ 

We have already remarked that, in the early days of the 
achromatic telescope, its progress was hindered by the difti- 
culty of making large disks of flint-glass. About the begin- 
ning of the present century, Guinand, a Swiss mechanic, after 
a long series of experiments, discovered a method by which 
he could produce disks of flint-glass of a size before unheard 
of. The celebrated Fraunhofer was then commencing busi- 
ness as an optician in Munich, and hearing of Guinand's suc- 
cess induced him to come to Munich and commence the man- 
ufacture of optical glass. Fraunhofer was a physicist of a 



138 



PRACTICAL ASTRONOMY. 




Fig. 43. — The great Melbourne reflector. T, the tube containing the great mirror near its 
lower end. Y, the small mirror throwing the light back to the eye-piece, y. C N, the 
polar axis. U, the counterpoise at the eud of the declinatiou axis. Z, the clock-work 
which moves the telescope by the joiuted rods z e e E, and the clamp F. 

high order, and made a more careful and exhaustive study of 
the optical qualities of glass, and the conditions for making 
the best telescope, than any one before him had ever attempted. 
With the aid of the large disks furnished by Guinand, he was 
able to carry the aperture of his telescopes up to ten inches. 
Dying in 1826, his successors, Merz and Mahler, of Munich, 
made two telescopes of fifteen inches aperture, which were 
then considered most extraordinary. One of these belongs 



GREAT REFRACTING TELESCOPES. 139 

to the Pulkowa Observatory, in Russia ; and the other was 
purchased by a subscription of citizens of Boston for the ob- 
servatory of Harvard University. 

No rival of the house of Fraunhofer in the construction of 
great refractors arose until he had been dead thirty years, and 
then it arose where least expected. In 1*40, Mr. Alvan Clark 
was a citizen of Cambridgeport, Massachusetts, unknown to 
fame, who made a modest livelihood by panning the self- 
taught art of portrait -painting, and beguiled his leisure by 
the construction of small telescopes. Though without the 
advantage of a mathematical education, he had a perfect 
knowledge of optical principles to just the extent necessary 
to enable him to make and judge a telescope. Having been 
led by accident to attempt the grinding of lenses, he soon pro- 
duced objectives equal in quality to any ever made, and. it 
he had been a citizen of any other civilized country, would 
have found no difficulty in establishing a reputation. But 
he had to struggle ten years with that neglect and incre- 
dulity which is the common lot of native genius in this coun- 
try ; and, extraordinary as it may seem, it was by a foreigner 
that his name and powers were first brought to the notice 
of the astronomical world. Rev. W. T£. Dawes, one of the 
leading amateur astronomers of England, and an active mem- 
ber of the Royal Astronomical Society, purchased an object- 
glass from Mr. Clark in 1S53. He found it so excellent that 
in the course of the next two or three years he ordered several 
others, and, finally, an entire telescope. He also made several 
communications to the Astronomical Society, giving lists of 
difficult double stars detected by Mr. Clark with telescopes of 
his own construction, and showing that Mr. Clark's objectives 
were almost perfect in definition. 

The result of this was that the American artist began to be 
appreciated in his own country ; and in 1S60 he received an 
order from the University of Mississippi, of which Dr. F. A. 
P. Barnard* was then president, for a refractor of eighteen 

* Xow President of Columbia College. New York City. 



140 PRACTICAL ASTRONOMY. 

inches aperture, which was three inches greater than the larg- 
est that had then been made. Before the glass was finished, 
it was made famous by the discovery of the companion of 
Sirius, a success for which the Lalande medal was awarded 
by the French Academy of Sciences. While this telescope 
was in progress, the civil war broke out, and prevented the 
party originally ordering it from taking it ; but it was soon 
sold to the Astronomical Society of Chicago, in which city it 
was mounted in 1863. The definition of this telescope is very 
fine ; but the defects of the dome in which it is mounted, and 
the want of means to support an astronomer, have greatly 
interfered with its efficiency. 

This instrument did not long retain its supremacy. The. 
firm of Thomas Cooke & Sons, of York, England, in 1870, 
mounted a refractor of twenty-five inches clear aperture for 
R. S. Newall, Esq., of Gateshead, England, of which the defi- 
nition is very good. This instrument was intended by its 
owner to be transported to some finer climate than that of 
England; but this project has not been put into execution. 
In the summer of 1874 it was used by Mr. Lockyer, in a study 
of Coggia's comet. 

During the time that these immense telescopes were being 
made on every hand, and after it was proved that telescopes of 
more than two feet aperture could be made, the National Ob- 
servatory of the United States had nothing better than an old 
Munich refractor of nine and a half inches, such as Fraunho- 
fer used to make early in the century. The attention of Con- 
gress was so forcibly called to this deficiency, and to the abili- 
ties of the firm of Alvan Clark & Sons to remedy it, that, in 
1870, a bill was passed authorizing the superintendent of the 
observatory to contract for a telescope of the largest size of 
American manufacture. The aperture agreed on was twenty- 
six inches, exceeding that of Mr. Newall's telescope by only 
one inch. It proved extremely difficult to obtain disks of 
rough glass even of this size, and more than a year elapsed 
after Messrs. Chance & Co. received the order from Mr. Clark 
before they were able to complete good disks of the required 



MAGNIFYING POWERS OF TELESCOPES. 141 

size. The glass arrived in December, 1871, and work was com- 
menced in January following. The labor of polishing the 
glasses was completed in October, 1872 ; the whole instrument 
was completed in a year more, and was finally mounted and 
ready for observation in November, 1873. The figure of this 
glass is almost perfect, its principal defect arising from the 
secondary aberration which is inseparable from a large re- 
fractor. It has been principally employed in observing the 
satellites of Saturn, Uranus, and Neptune, with the view of de- 
termining the masses of these planets. 

§ 7. The Magnifying Powers of the Two Classes of Telescopes. 

Questions which now very naturally arise are, Which of the 
two classes of telescopes we have described is the more power- 
ful, the reflector or the refractor? and is there any limit to the 
magnifying power of either ? To these questions it is difficult 
to return a decided answer, because each class has its peculiar 
advantages, and in each class many difficulties lie in the way 
of obtaining the highest magnifying power. The fact is, that 
very exaggerated ideas of the magnifying power of great tele- 
scopes are entertained by the public. It will, therefore, be 
instructive to state what the circumstances are which prevent 
these ideas from being realized, and what the conditions are 
on which the seeing power of telescopes depends. 

We note, first, that when we look at a luminous point — a star, 
for instan ce — without a telescope, we see it by the aid of the 
cone of light which enters the pupil of the eye. The diameter 
of the pupil being about one-fifth of an inch, as much light 
from the star as falls on a circle of this diameter is brought to 
a focus on the retina, and unless this quantity of light is suffi- 
cient to be perceptible, the star will not be seen. Now, we 
may liken the telescope to a " Cyclopean eye," of which the 
object-glass is the pupil, because, by its aid, all the light which 
falls on the object-glass is brought to a focus on the retina, 
provided that a sufficiently small eye-piece is used. Of course, 
we must except that portion of the light which is lost in pass- 
ing through the glasses. Since the quantity of light which 



142 PRACTICAL ASTRONOMY. 

falls on a surface is proportional to the extent of the surface, 
and therefore to the square of its diameter, it follows that, 
because a telescope of one -inch clear aperture has live times 
the diameter of the pupil, it will admit 25 times the light; a 
six-inch will admit 900 times the light which the pupil will ; 
and so with any other aperture. A star viewed with the 
telescope will, therefore, appear brighter than to the naked 
eye in proportion to the square of the aperture of the in- 
strument. But the star will not be magnified like a planet, 
because a point is only a point, no matter how often we mul- 
tiply it. It is true that a bright star in the telescope some- 
times appears to have a perceptible disk; but this is owing to 
various imperfections of the image, having their origin in the 
air j the instrument, and the eye, all of which have the effect of 
slightly scattering a portion of the light which comes from the 
star. Hence, with perfect vision the apparent brilliancy of a 
star will be proportional to the square of the aperture of the 
telescope. It is said that Sir William Herschel, at a time when 
by accident his telescope was so pointed that Sirius was about 
to enter its field of view, was first apprised of what was com- 
ing by the appearance of a dawn like the morning. The light 
increased rapidly, until the star itself appeared with a dazzling 
splendor which reminded him of the rising sun. Indeed, in 
any good telescope of two feet aperture or upwards, Sirius is 
an almost dazzling object to an eye which has rested for some 
time in darkness. 

But in order that all the light which falls on the object- 
glass, or mirror, of a telescope may enter the pupil of the eye, 
it is necessary that the magnifying power be at least equal to 
the ratio which the aperture of the telescope bears to that of 
the pupil. The latter is generally about one-fifth of an inch. 
We must, therefore, employ a magnifying power of at least 
five for every inch of aperture, or we will not get the full ad- 
vantage of our object-glass. The reason of this will be appar- 
ent by studying Fig. 29, p. 109, from which it will be seen that 
a pencil of parallel rays falling on the object-glass, and pass- 
ing through the eye-piece, will be reduced in diameter in the 



MAGXIFYIXG POWERS OF TELESCOPES. 113 

ratio of the focal distance of the objective to that of the eye- 
piece, which is the same as the magnifying power. For in- 
stance, if to a twenty-four-inch telescope we attached an eve- 
piece so large that the magnifying power was only 4S, and 
pointed it at a bright star, the " emergent pencil " of rays from 
the eye-piece would be half an inch in diameter, and the whole 
of them could not possibly enter the pupil. By increasing the 
magnifying power, we would increase the apparent brilliancy 
of the star, until we reached the power 120, after which no 
further increase of brilliancy would be possible. 

All this supposes that we are viewing a star or other lumi- 
nous point. If the object has a sensible surface, like the moon. 
or a large nebula, and we consider its apparent superficial 
brilliancy, the case will be in part reversed. The object will 
then appear equally illuminated, with all powers below five 
for each inch of aperture, but will begin to grow darker when 
we pass above that limit. The reason of this is, that as we 
increase the magnifying power the light is spread over a larger 
surface of the retina, and is thus enfeebled. So long as our 
magnifying power is below the limit, the increased quantity 
of light which enters the pupil by an increase of magnifying 
power just compensates for the greater surface over which it 
is spread, so that the brilliancy is constant. Above the limit 
of five to the inch, the surface over which the light is spread, 
or the apparent magnitude of the object, still increases with 
the magnifying power, but there is no increase of light ; hence, 
the object looks fainter. "What may at first sight seem para- 
doxical is, that the degree of illumination to which we now 
refer can never be increased by the use of the telescope, but. 
at the best, will be the same as to the naked eye. Indeed, 
as some light is necessarily lost in passing through any tele- 
scope, the illumination is always less with the telescope. AVith 
the best reflectors of speculum metal, the illumination will be 
reduced to one-half, or less, if the polish is not perfect ; and 
with refractors it will be reduced to seven or ei^ht tenths. As 
examples of these conclusions, the sky can never be made to 
appear as bright through a telescope as to the naked eye ; the 

11 



144 PRACTICAL ASTRONOMY. 

moon or a large nebula will appear more brightly illuminated 
through a refracting telescope than through a reflector. If 
the object is a very brilliant one, like the sun or Yenus, the 
loss of brilliancy by magnifying, which we have described, will 
not cause any inconvenience ; but the outer planets and many 
of the nebulae are so faintly illuminated that a magnifying 
power many times exceeding the limit cannot be used with 
advantage. 

Still another cause which places a limit to the power of 
telescopes is diffraction. When the "emergent pencil" is 
reduced below -^ of an inch in diameter — that is, when the 
magnifying power is greater than 50 for every inch of aper- 
ture of the object-glass — the outlines of every object observed 
become confused and indistinct, no matter how bright the il- 
lumination or how perfect the glass may be. The effect is the 
same as if we looked through a small pin-hole in a card, an 
experiment which anyone may try. This effect is owing to 
the diffraction of the light at the edge of the object-glass or 
mirror, and it increases so rapidly with the magnifying power 
that when we carry the latter above 100 to the inch, the in- 
crease of indistinctness neutralizes the increase of power. If, 
then, we multiply the aperture of the telescope in inches by 
100, we shall have a limit beyond which there is no use in 
magnifying. Indeed, it is doubtful if any real advantage is 
gained beyond 60 to the inch. In a telescope of two feet (24 
inches) aperture this limit would be 2400. Such a limit can- 
not be set with entire exactness ; but, even under the most fa- 
vorable circumstances, the advantage in attempting to surpass 
a power of 70 to the inch will be very slight. 

The foregoing remarks apply to the most perfect telescopes, 
used under the most favorable circumstances. But the best 
telescope has imperfections which would nearly always pre- 
vent the use of the highest magnifying powers in astronomical 
observations. In the refracting telescope the principal defect 
arises from the secondary aberration already explained, which, 
arising from an inherent quality of the glass itself, cannot be 
obviated by perfection of workmanship. In the case of the re- 



MAGNIFYING POWERS OF TELESCOPES. 145 

flector, the corresponding difficulty is to keep the mirror in per- 
fect figure in every position. As the telescope is moved about, 
the mirror is liable to bend, through its own weight and elas- 
ticity, to such an extent as greatly to injure or destroy the im- 
age in the focus; and, though this liability is greatly dimin- 
ished by the plan now adopted, of supporting the mirror on a 
system of levers or on an air-cushion, it is generally trouble- 
some, owing to the difficulty of keeping the apparatus in order. 
If we compare the refracting and reflecting telescopes which 
have hitherto been made, it is easy to make a summary of 
their relative advantages. If properly made and attended to, 
the refractor is easy to manage, convenient in use, and al- 
ways in order for working with its full power. If its greatest 
defect, the secondary spectrum, cannot be diminished by skill, 
neither can it be increased by the want of skill on the part of 
the observer. So important is this certainty of operation, that 
far the greater part of the astronomical observations of the 
present century have been made with refractors, which have 
always proved themselves the best working instruments. Still, 
the defects arising from the secondary spectrum are inherent 
in the latter, and increase with the aperture of the glass to 
such an extent that no advantage can ever be gained by carry- 
ing the diameter of the lenses beyond a limit which may be 
somewhere between 30 and 36 inches. On the otKer hand, 
when we consider mere seeing-power, calculation at least gives 
the preference to the reflector. It is easy to compute that 
Lord Rosse's " Leviathan," and the four-foot reflectors of Mr. 
Lassell and of the Paris and Melbourne observatories, must 
collect from two to four times the light of the great Washing- 
ton telescope. But when, instead of -calculation, we inquire 
what difficult objects have actually been seen with the two 
classes of instruments, the result seems to indicate that the 
greatest refractor is equal in optical power to the great reflect- 
ors. No known object seen with the latter is too faint to be 
seen with the former. Why this discrepancy between the 
calculated powers of the great reflectors and their actual per- 
formance ? The only causes we can find for it are imperfec- 



146 PEACTICAL ASTRONOMY. 

tions in the figure and polish of the great mirrors. The great 
refractors are substantially perfect in their workmanship; the 
reflectors do not appear to be perfect, though what the imper- 
fections may be, it is impossible to say with entire certainty. 
Whether the great telescope of the future shall belong to the 
one class or the other must depend upon whether the imper- 
fections of the reflecting mirror can be completely overcome. 
Mr. Grubb, the maker of the great Melbourne telescope, thinks 
he has completely succeeded in this, so as to insure a mirror 
of six, seven, or even eight feet in diameter which shall be as 
perfect as an object-glass. If he is right — and there is no 
mechanician whose opinion is entitled to greater confidence — 
then he has solved the problem in favor of the reflector, so far 
as optical power is concerned. But so large a telescope will 
be so difficult to manipulate, that we must still look to the re- 
fractor as the working instrument of the future as well as of 
the past; though, for the discovery and examination of very 
faint objects, it may be found that the advantage will all be 
on the side of the future great reflector. 

The great foe to astronomical observation is one which 
people seldom take into account, namely, the atmosphere. 
When we look at a distant object along the surface of the 
ground on a hot summer day, we notice a certain waviness of 
outline, accompanied by a slight trembling. If we look with 
a telescope, we shall find this waving and trembling magnified 
as much as the object is, so that we can see little better with 
the most powerful telescope than with the naked eye. The 
cause of this appearance is the mixing of the hot air near the 
ground with the cooler air above, which causes an irregular 
and constantly changing refraction, and the result is that as- 
tronomical observations requiring high magnifying power can 
very rarely be advantageously made in the daytime. , By 
night the air is not so much disturbed, yet there are always 
currents of air of slightly different temperatures, the crossing 
and mixing of which produce the same effects in a small de- 
gree. To such currents is due the twinkling of the stars: 
and we may lay it down as a rule, that when a star twinkles 



MAGNIFYING POWERS OF TELESCOPES. 147 

the finest observation of it cannot be made with a telescope of 
high power. Instead of presenting the appearance of a bright, 
well-defined point, it will look like a blaze of light flaring 
about in every direction, or like a pot of molten boiling metal ; 
and the higher the magnifying power, the more it will flare 
and boil. The amount of this atmospheric disturbance varies 
greatly from night to night, but it is never entirely absent. 
If no continuous disturbance of the image could be seen with 
a power of 400, most astronomers would regard the night as a 
very good one; and nights on which a power of more than 
1000 can be advantageously employed are quite rare, at lea>t # 
in this climate. 

It has sometimes been said that Sir William Ilerschel em- 
ployed a power as high as 6000 with one of his great tele- 
scopes, and, on the strength of this, that the moon may have 
been brought within an apparent distance of forty miles. If 
such a power was used on the moon, we must suppose, nut 
merely that the moon was seen as if at the distance of forty 
miles, even if Ilerschel used his largest telescope — that of 
four feet aperture — but that the vision would be the same as 
if he had looked through a pin-hole y^r of au inch in diam- 
eter, and through several yards of running water, or many 
miles of air. It is doubtful whether the moon has ever been 
seen with any telescope so well as it could be seen with the 
naked eye at a distance of 500 miles. If such has been the 
case, we may be sure that the magnifying power did not ex- 
ceed 1000. 

If seeing depended entirely on magnifying power, we could 
not hope to gain much by further improvement of the tele- 
scope, unless we should mount our instrument in some place 
where there is less atmospheric disturbance than in the re- 
gions where observatories have hitherto been built. It is sup- 
posed that, on the mountains or table-lands in the western and 
south-western regions of North America, the atmosphere is 
clear and steady in an extraordinary degree ; and if this sup- 
position is entirely correct, a great gain to astronomy might 
result from establishing an observatory in that region. 



148 PEACTICAL ASTRONOMY. 



CHAPTER II. 

APPLICATION OF THE TELESCOPE TO CELESTIAL MEASUKEMENTS. 

§ 1. Circles of the Celestial Sphere, and their Relations to Positions 

on the Earth. 

In the opening chapter of this work it was shown that all 
the heavenly bodies seem to lie and move on the surface of a 
sphere, in the interior of which the earth and the observer are 
placed. The operations of Practical Astronomy consist large- 
ly in determining the apparent positions of the heavenly bod- 
ies on this sphere. These positions are denned in a way anal- 
ogous to that in which the position of a city or a ship is de- 
fined on the earth, namely, by a system of celestial latitudes 
and. longitudes. That measure which, in the heavens, corre- 
sponds most nearly to terrestrial longitude is called Right As- 
cension, and that which corresponds to terrestrial latitude is 
called Declination. 

In Pig. 45 let the globe be the celestial sphere, represented 
as if viewed from the outside by an observer situated towards 
the east, though we necessarily see the actual sphere from the 
centre. Pis the north pole, AB the horizon, Q the south pole 
(invisible in northern latitudes because below the horizon), EF 
the equator, Z the zenith. The meridian lines radiate from 
the north pole in every direction, cross the equator at right 
angles, and meet again at the south pole, just like meridians 
on the earth. The meridian from which right ascensions are 
counted, corresponding in this respect to the meridian of 
Greenwich on the surface of the earth, is that which passes 
through the vernal equinox, or point of crossing of the equa- 
tor and ecliptic. It is called the first meridian. Three bright 



CIRCLES OF THE CELESTIAL SPHERE. 



149 



stars near which this meridian now passes may be seen during 
the autumn : they are a Andromedae and y Pegasi, on Maps 
II. and V., and /3 Cassiopeia^, on Map I. The right ascension 
of any star on this meridian is zero, and the right ascension 
of any other star is measured by the angle which the merid- 
ian passing through it makes with the first meridian, this angle 
being always counted towards the east. For reasons which 
will soon be explained, right ascension is generally reckoned, 
not in degrees, but in hours, minutes, and seconds of time. 



"h U n& 




I J is the ecliptic, crossing the equator at its point of inter- 
section with the first meridian, and making an angle of 23^° 
with it. The declination of a star is its distance from the 
celestial equator, whether north or south, exactly as latitude 
on the earth is distance from the earth's equator. Thus, when 
the right ascension and declination of a heavenly body are 
given, the astronomer knows its position in the celestial sphere, 
just as we know the position of a city on the earth when its 
longitude and latitude are given. 

It must be observed that the declinations of the heavenly 



150 PRACTICAL ASTRONOMY. 

bodies are, in a certain sense, referred to the earth. In as- 
tronomy the equator is regarded as a plane passing through 
the centre of the earth, at right angles to its axis, and dividing 
it into two hemispheres. The line where this plane intersects 
the surface of the earth is our terrestrial, or geographical, equa- 
tor. If an observer standing on the geographical equator im- 
agines this plane running east and west, and cutting into and 
through the earth, where he stands he will have the astro- 
nomical equator, which differs from the geographical equator 
only in being the plane in which the latter is situated. Now 
imagine this plane continued in every direction without limit 
till it cuts the infinite celestial sphere as in Fig. 17, page 62. 
The circle in which it intersects this sphere will be the celes- 
tial equator. It will pass directly over the head of the ob- 
server at the equator. 

There is a general correspondence between latitude on the 
earth and declination in the heavens, which may be seen by 
referring to the same figure. Here the reader must conceive 
of the earth as a globe, ep, situated in the centre of the celes- 
tial sphere, EPQS, which is infinitely larger than the earth. 
The plane represented by EQ is the astronomical equator, di- 
viding both the earth and the imaginary celestial sphere into 
two equal hemispheres. Suppose, now, that the observer, in- 
stead of standing under the equator, is standing under some 
other parallel, say that of 45° N. (Being in this latitude means 
that the plumb-line where he stands makes an angle of 45° 
with the plane of the equator.) The point over his head will 
then be in 45° celestial declination. If we imagine a pencil 
of infinite length rising vertically where the observer stands 
so that its point shall meet the celestial sphere in his zenith, 
and if, as the earth performs its diurnal revolution on its axis, 
we imagine this pencil to leave its mark on the celestial sphere, 
this mark will be the parallel of 45° N. declination, or a cir- 
cle everywhere equally distant from the equator and from the 
pole. The same observer will see the celestial pole at an eleva- 
tion equal to his latitude, that is, at the angle 45°. We have now 
the following rules for determining the latitude of a place : 



CIRCLES OF THE CELESTIAL SPHERE. 151 

1. The latitude is equal to the declination of the observer's zenith. 

2. It is also equal to the cdtitude of the pole above his horizon. 
Hence, if the astronomer at any unknown station wishes to 

determine his latitude, he has only to find what parallel of 
declination passes through his zenith, the latter being marked 
by the direction of the plumb-line, or by the perpendicular to 
the, surface of still water or quicksilver. If he finds a btar 
passing exactly in his zenith, and knows its declination, he has 
his latitude at once, because it is the same as the star's dec- 
lination. Practically, however, an observer will never find a 
known star exactly in his zenith; he must therefore find at 
what angular distance from the zenith a known star passes his 
meridian, and by adding or subtracting this distance from the 
star's declination he has his latitude. If he does not know 
the declination of any star, he measures the altitudes above 
the horizon at which any star near the pole passes the merid- 
ian, both above the pole and under the pole. The mean of 
the two gives the latitude. 

Let us now consider the more complex problem of deter- 
mining longitudes. If the earth did not revolve, the observ- 
er's longitude would correspond to the right ascension of his 
zenith in the same fixed manner that his latitude corresponds 
to its declination. But, owing to the diurnal motion, there is 
no such fixed correspondence. It is therefore necessary to 
have some means of representing the constantly varying rela- 
tion. 

Wherever on the earth's surface an observer may stand, his 
meridian, both terrestrial and celestial, is represented astronom- 
ically by an imaginary plane similar to the plane of the equa- 
tor. This plane is vertical to the observer, and passes through 
the poles. It divides the earth into two hemispheres, and is 
perpendicular to the equator. In Fig. 17, the celestial and ter- 
restrial spheres are supposed to be cut through by this plane ; 
it cuts the earth when the observer stands in a line running 
north and south from pole to pole, and thus forms a terrestrial 
meridian. The same plane intersects the celestial sphere in a 
great circle, which, rising above the observer's horizon in the 



152 PRACTICAL ASTRONOMY. 

north, passes through the pole and the zenith, and disappears at 
the south horizon. Two observers north and south of each 
other have the same meridian ; but in different longitudes they 
have different meridians, which, however, all pass through each 
pole. 

In consequence of the earth's diurnal motion, the meridian 
of every place is constantly moving among the stars in such a 
way as to make a complete revolution in 23 hours 56 minutes 
4.09 seconds. The reader will find it more easy to conceive 
of the celestial sphere as revolving from east to west, the ter- 
restrial meridian remaining at rest ; the effect being geomet- 
rically the same whether we conceive of the true or the ap- 
parent motion. There are, then, two sets of meridians on 
the celestial sphere. One set (that represented in Fig. 45) is 
fixed among the stars, and is in constant apparent motion 
from east to west with the stars, while the other set is fixed 
by the earth, and is apparently at rest. 

As differences of latitude are measured by angles in the 
heavens, so differences of terrestrial longitude are measured by 
the time it takes a celestial meridian to pass from one terres- 
trial meridian to another ; while differences of right ascension 
are measured by the time it takes a terrestrial meridian to 
move from one celestial meridian to another. Ordinary solar 
time would, however, be inconvenient for this measure, because 
a revolution does not take place in an exact number of hours. 
A different measure, known as sidereal time, is therefore in- 
troduced. The time required for one revolution of the celes- 
tial meridian is divided into 24 hours, and these hours are 
subdivided into minutes and seconds. Sidereal noon at any 
place is the moment at which the vernal equinox passes the 
meridian of that place, and sidereal time is counted round 
from hour to 24 hours, when the equinox will have returned 
to the meridian, and the count is commenced over again. 
Since right ascensions in the heavens are counted from the 
equinox, when it is sidereal noon, or hour, all celestial ob- 
jects on the meridian of the place are in 0° of right ascension. 
At 1 hour sidereal time, the meridians have moved 15°, and 



CIRCLES OF THE CELESTIAL SPHERE. 158 

objects now on the meridian are in 15° of right ascension. 
Throughout its whole diurnal course the right ascension of the 
meridian constantly increases at the rate of 15° per hour, so 
that the right ascension is always found by multiplying the 
sidereal time by 15. To avoid this constant multiplication, it 
is customary in astronomy to express both right ascensions and 
terrestrial longitudes by hours. Thus the Pleiades are said to 
be in 3 hours 40 minutes right ascension, meaning that they are 
on the meridian of any place at 3 hours 40 minutes sidereal 
time. The longitude of the Washington Observatory from 
Greenwich is 77° 3'; but in astronomical language the longi- 
tude is said to be 5 hours 8 minutes 12 seconds, meaning that 
it takes 5 hours 8 minutes 12 seconds for any celestial merid- 
ian to pass from the meridian of Greenwich to that of Wash- 
ington. In consequence, when it is hour, sidereal time at 
Washington, it is 5 hours 8 minutes 12 seconds sidereal time 
at Greenwich. 

About March 22d of every year, sidereal hour occurs very 
nearly at noon. On each successive day it occurs about 3 min- 
utes 56 seconds earlier, which in the course of a year brings 
it back to noon again. Since the sidereal time gives the posi- 
tion of the celestial sphere relatively to the meridian of any 
place, it is convenient to know it in order to find what stars 
are on the meridian. The following table shows the sidereal 
time of mean, or ordinary civil, noon at the beginning of each 
month : 

Hrs. Min. 

January 18 45 

February 20 47 

March 22 37 

April 40 

May 2 38 

June 4 40 



July 6 38 

August S 40 

September 10 43 

October 12 41 

November 14 43 

December 16 42 



The sidereal time at any hour of the year may be found 
from the preceding table by the following process within a 
very few minutes: To the number of the preceding table 
corresponding to the month add 4 minutes for each day of 
the month, and the hour past noon. The sum of these num- 



154 PRACTICAL ASTRONOMY. 

bers, subtracting 24 hours if the sum exceeds that quantity, 
will give the sidereal time. As an example, let it be required 
to find the sidereal time corresponding to November 13th at 
3 a.m. This is 15 hours past noon. So we have 

Hrs. Min. 

November, from table 14 43 

13 daysX4 52 

Past noon 15 

Sum 30 35 

Subtract 24 

Sidereal time required 6 35 

The sidereal time obtained in this way will seldom or never 
be more than five minutes in error during the remainder of 
this century. In every observatory the principal clock runs 
by sidereal time, so that by looking at its face the astronomer 
knows what stars are on or near the meridian. Having the 
sidereal time, the stars which are on the meridian may be 
found by reference to the star maps, where the right ascen- 
sions are shown on the borders of the maps. 

§ 2. The Meridian Circle, and its Use. 

As a complete description of the various sorts of instru- 
ments used in astronomical measurements, and of the modes 
of using them, would interest but a small class of readers, 
we shall confine ourselves for the present to one which may 
be called the fundamental instrument of modern astronomy, 
the application of which has direct and immediate reference 
to the circles of the celestial sphere described in the preceding 
section. This one is termed the Meridian Circle, or Transit Cir- 
cle. Its essential parts are a moderate-sized telescope balanced 
on an axis passing through its centre, with a system of fine 
lines in the eye-piece ; one or two circles fastened on the axis, 
revolving with the telescope, and having degrees and subdi- 
visions cut on their outer edges; and a set of microscope mi- 
crometers for measuring between the lines so cut. It is abso- 
lutely necessary that every part of the instrument shall be of 
the most perfect workmanship, and that the masonry piers on 



THE MERIDIAN CIRCLE, AND ITS USE. 



155 



which it is mounted shall be as stable as it is possible to make 
them. 

There are many differences of detail in the construction 
and mounting of different meridian circles, but they all turn 
on an east and west horizontal axis, and therefore the telescope 
moves only in the plane of the meridian. Fig. 45 shows the 




•Fio. 45.— The Washington transit circle. 

construction of the great circle in the Naval Observatory, 
Washington. The marble piers, PP, are supported on a mass 
of masonry under the floor, the bottom of which is twelve feet 
below the surface of the ground. The middle of the telescope 
is formed of a large cube, about fifteen inches on each side. 
From the east and west side of this cube extend the trunn- 
ions, which are so large next the cube as to be nearly conical 
in shape. The outer ends terminate in finely ground steel 
pivots two and a half inches in diameter, which rest on brass 
V's firmly fixed to heavy castings set into the piers with hy- 



156 



PRACTICAL ASTRONOMY. 



draulic cement. In order that the delicate pivots may not 
be worn by the whole weight of the instrument resting on 
them, the counterpoises, BB, support all the weight except 30 
or 40 pounds. Near the ends of the axis are the circles, seen 
edgewise, which are firmly screwed on the trunnions, and there- 
fore turn with the instrument. Each pier carries four arms, 
and each of these arms carries a microscope, marked m, hav- 
ing in its focus the face of the circle on which the lines are 
cut. These lines divide the circle into 360°, and each degree 
into thirty spaces of two minutes each, so that there are 10,800 
lines cut on the circle. They are cut in a silver band, and are 
so fine as to be invisible to the naked eye unless the light is 
thrown upon them in a particular way. On each side of the 
instrument, in a line with the axis, is a lamp which throws 
light into the telescope so as to illuminate the field of view. 
Reflecting prisms inside of the pier throw some of the light 
upon those points of the circle which are viewed by the mi- 
croscopes, so as to illuminate the fine divisions on the circle. 
Being thus limited in its movements, an object can be seen 
with the telescope only when on, or very near, the meridian. 
The sole use of the instrument is to observe the exact times 
at which stars cross the meridian, and their altitudes above 
the horizon, or distances from the zenith, at the time of cross- 
ing. To give precision to these observations, the eye-piece of 
the instrument is supplied with a system of fine black lines, 

usually made of spider's web, as 
shown in Fig. 46. These lines 
are set in the focus, so that the 
image of a star crossing the me- 
ridian passes over them. The 
middle vertical spider line marks 
the meridian ; and to find the 
time of meridian transit of a star 
it is only necessary to note the 
moment of passage of its image 
, over this line. But, to give great- 

Fig. 46.— Spider lines in field of view of # r . 

a meridian circle. er precision and certainty to his 




THE MERIDIAN CIRCLE, AND ITS USE. 157 

observation, the astronomer generally notes the moments of 
transit over five or more lines, and takes the average of them 
all. 

Formerly the astronomer had to find the times of transit by 
listening to the beat of his sidereal clock, counting the sec- 
onds, and estimating the tenths of a second at which the tran- 
sit over a line took place. If, for instance, he should find that 
the star had not reached the line when the tick of twenty- 
three seconds was heard, but crossed before the twenty-fourth 
second was ticked, he would know that the time was twenty- 
three seconds and some fraction, and would have to estimate 
what that fraction was. A skilful observer will generally 
make this estimate within a tenth of a second, and will only 
on rare occasions be in error by as much as two tenths. 

Shortly after the introduction of the electric-telegraph, the 
American astronomers of that day introduced a much easier 
method of determining the time of transit of a star, by means 
of the electro-chronograpli. As now made, this instrument con- 
sists of a revolving cylinder, having a sheet of paper wrapped 
around it, and making one revolution per minute. A pen 
or other marker is connected with a telegraphic apparatus in 
such a way that whenever a signal is sent to the pen it makes 
a mark on the moving paper. This pen moves lengthwise of 
the cylinder at the rate of about an inch in ten minutes, so 
that, in consequence of the turning of the cylinder on its axis, 
the marks of the pen will be' along a spiral, the folds of which 
are one-tenth of an inch apart. The galvanic circuit which 
works the pen is connected with the sidereal clock, so that the 
latter causes the pen to make a signal every second. The 
same pen may be worked by a telegraphic key in the hand 
of the observer. The latter, looking into his telescope, and 
watching the approach of the image of the star to each wire, 
makes a signal at the moment at which the star crosses. This 
signal is recorded on the chronograph in its proper place 
among the clock signals, from which it may be distinguished 
by its greater strength. The record is permanent, and the 
sheet may be taken off and read at leisure, the exact tenth of 



15S PRACTICAL ASTRONOMY. 

a second at which each signal was made being seen by its 
position among the clock signals. The great advantages of 
this method are, that great skill and practice are not required 
to make good observations, and that the observer need not see 
either the clock or his book, and can make a great number of 
observations in the course of the evening which may be read 
off at leisure. In the case of the most skilful observers there 
is no great gain in accuracy, for the reason that they can esti- 
mate the fraction of a second by the eye and ear with nearly 
the same accuracy that they can give the signal. 

The zenith distance of the star, from which its declination 
is determined, is observed by having in the reticule a hori- 
zontal spider line which is made to bisect the image of the 
star as it passes the meridian line. The observer then goes to 
the microscopes, ascertains what lines cut on the circle are un- 
der them, and what number of seconds the nearest line is from 
the proper point in the field of the microscope. The mean of 
the results from the four microscopes is called the circle-reading, 
and can be determined within two or three tenths of a second 
of arc, or even nearer, if all the apparatus is in the best order. 
The minuteness of this angle may be judged by the circum- 
stance that the smallest round object a keen eye can see sub- 
tends an angle of about forty seconds. 

We have described only the leading operations necessary in 
determinations with a meridian circle. To complete the de- 
termination of the position of a star as accurately as a prac- 
tised observer can bisect it with the spider line is a much more 
complicated matter, owing to the unavoidable errors and im- 
perfections of his instrument. It is impossible to set the lat- 
ter in the meridian with mathematical precision, and, if it were 
done, it would not remain so a single day. When the astron- 
omer comes to tenths of seconds, he has difficulties to contend 
with at every step. The effects of changes of temperature 
and motions of the solid earth on the foundations of his in- 
strument are such as to keep it constantly changing ; his clock 
is so far from going right that he never attempts to set it per- 
fectly right, but only determines its error from his observa- 



DETERMINATION OF TERRESTRIAL LONGITUDES. 159 

tions. Every observation must, therefore, be corrected for a 
number of instrumental errors before the result is accurate, 
an operation many times more laborious than merely making 
the observation. 

§ 3. Determination of Terrestrial Longitudes. 

The telegraphic mode of recording observations, described 
in the last section, affords a method of determining differences 
of longitude between places connected by telegraph of ex- 
traordinary elegance and perfection. We have already shown 
that the difference of longitude between two points is mi 
ured by the time it takes a star to move from the meridian of 
the easternmost point to that of the westernmost point. We 
have also explained in the last section how an observer with a 
meridian circle determines and records the passage of a star 
over his meridian within a tenth of a second. Since the ze- 
nith distance of the star is not required in this observation, the 
circles and microscopes may be dispensed with, and the instru- 
ment is then much simpler in construction, and is termed a 
Transit Instrument. When the observer makes a telegraphic 
record of the moment of transit of a star by striking a key in 
the manner described, it is evident that the electro -chrono- 
graph on which his taps are recorded may be at any distance 
to which the electric current can carry his signal. It may. 
therefore, be in a distant city. There is no difficulty in a 
Washington observer recording his observations in Cincinnati. 

On this system, the mode of operation is about as follows : 
the Washington and Cincinnati stations each has its transit in- 
strument, its observer, and its chronograph ; but the chrono- 
graphs are connected by telegraph, so that any signal made 
by either observer is recorded on both chronographs. As 
the Washington observer sees a star previously agreed on pass 
over the lines in the focus of his instrument, he makes sig- 
nals with his telegraphic key, which are recorded both on his 
own chronograph and on that of Cincinnati. When the star 
readies the meridian of the latter city, the observer there sig- 
nals the transit of the star in like manner, and the moment 

12 



160 PRACTICAL ASTRONOMY. 

of passage over each line in the focus of his instrument is 
recorded, both in Cincinnati and Washington. The elapsed 
time is then found by measuring off the chronograph sheets. 

The reason for having all the observations recorded on both 
chronographs is that the results may be corrected for the time 
it takes the electric current to pass between the two cities, 
which is quite perceptible at great distances. In consequence 
of this " wave-time," the Washington observation will be re- 
corded a little too late at Cincinnati, so that the difference of 
longitude on the Cincinnati chronograph will be too small. 
The Cincinnati observation, which comes last, being recorded 
a little too late at Washington, the difference of time on the 
Washington chronograph will be a little too great. The mean 
of the results on the two chronographs will be the correct 
longitude, while their difference will be twice the time it takes 
the electric current to pass between the two cities. The re- 
sults thus obtained for the velocity of electricity are by no 
means accordant, but the larger number do not differ very 
greatly from 8000 miles per second. 

A celestial meridian moves over the earth's surface at the 
rate of fifteen degrees an hour, or a minute of arc in four sec- 
onds of time. More precisely, this is the rate of rotation of 
the earth. The length of a minute of arc in longitude de- 
pends on the latitude. It is about 6000 feet, or a mile and a 
sixth at the equator, but diminishes whether we go north or 
south, owing to the approach of the meridians on the globular 
earth, as can be seen on a globe. In the latitude of our Mid- 
dle States it is about 4600 feet, so that the surface of the earth 
there moves over 1150 feet a second. At the latitude of 
Greenwich it is 3800 feet, so that the motion is 950 feet per 
second. Two skilful astronomers, by making a great num- 
ber of observations, can determine the time it takes the stars 
to pass from one meridian to another within one or two hun- 
dredths of a second of time, and can therefore make sure of 
the difference of longitude between two distant cities within 
six or eight yards. 

Of late the telegraphic method of determining longitudes 



DETERMINATION OF TERRESTRIAL LONGITUDES. 161 

has been applied in a way a little different, though resting on 
the same principles. Instead of recording the transits of stars 
on both chronographs, each observer determines the error of 
bis clock by transits of stars of which the right ascension has 
been carefully determined. Each clock is then connected with 
both chronographs by means of the telegraphic lines, and made 
to record its beats for the space of a few minutes only. Thus 
the difference between the sidereal times at the two stations 
for the same moment of absolute time can be found, and this 
difference is the difference of longitude in time. A few years 
ago, when the difference of longitude between points on the 
Atlantic and Pacific coasts was determined by the ( 
Survey, a clock in Cambridge was made to record its beats on 
a chronograph in San Francisco, and nV In 1866, as 

soon as the Atlantic cable had been successfully laid, Dr. B. A. 
Gould went to Europe, under the auspices of the Coast Survey. 
to determine the difference of longitude between Europe and 
America. Owing to the astronomical importance of this de- 
termination, it has since been twice repeated, once under the 
direction of Mr. Dean, and, lastly, under that of Mr. Hilgard, 
both of the Survey. These three campaigns gave the follow- 
ing separate results for the difference of longitude between 
the Koyal Observatory, Greenwich, and the Naval Observato- 
ry, Washington : 

Hrs. Min. Sec. 

Dr. Gould, 18G7 5 8 12.11 

Mr. Dean, 1870 :» S 12.16 

Mr. Hilgard, 1872 5 8 12.09 

The extreme difference, it will be seen, is less than a tenth of 
a second, and would probably have been smaller but for the 
numerous difficulties attendant on a determination through a 
long ocean cable, which are much greater than through a land 
line. 

The use of the telegraph for the determination of longitude 
is necessarily limited, and other methods must therefore gen- 
erally be used. The general problem of determining a longi- 
tude, whether that of a ship upon the ocean or of a station 



162 PRACTICAL ASTRONOMY. 

upon the land, depends on two requirements : (1) a knowledge 
of the local time at the station, and (2) a knowledge of the 
corresponding time at Greenwich, Washington, or some other 
standard meridian. The difference of these two represents 
the longitude. 

The first determination, that of the local time, is not a diffi- 
cult problem when the utmost accuracy is not required. We 
have already shown how it is determined with a transit instru- 
ment. But this instrument cannot be used at all at sea, and 
is somewhat heavy to carry and troublesome to set up on the 
land. For ships and travellers it is, therefore, much more con- 
venient to use a sextant, by which the altitude of the sun or of 
a star above the horizon can be measured with very little time 
or trouble. To obtain the time, the observation is made, not 
when the object is on the meridian, but when it is as nearly as 
practicable east or west. Having found the altitude, the calcu- 
lation of a spherical triangle from the data given in the Nau- 
tical Almanac at once gives the local time, or the error of the 
chronometer on local time. 

The difficult problem is to determine the Greenwich time. 
So necessary to navigation is some method of doing this, that 
the British Government long had a standing offer of a reward 
of £10,000 to any one who would find a successful method 
of determining the longitude at sea. When the office of As- 
tronomer Royal was established, which was in 1675, the duty 
of the incumbent was declared to be " to apply himself with 
the most exact care and diligence to the rectifying the Ta- 
bles of the Motions of the Heavens, and the places of the 
Fixed Stars, in order to find out the so much desired Longi- 
tude at Sea for the perfecting the Art of Navigation." The 
reward above referred to was ultimately divided between an 
astronomer, Tobias Mayer, who made a great improvement in 
the tables of the moon, and a watch-maker who improved the 
marine chronometer. 

The moon, making her monthly circuit of the heavens, may 
be considered a sort of standard clock from which the astron- 
omer can learn the Greenwich time, in whatever part of the 



DETERMINATION OF TERRESTRIAL LONGITUDES. 168 

world he may find himself. This he does by observing her po- 
sitions among the stars. The Nautical Almanac gives the pre- 
dicted distance of the moon from certain other bodies — sun, 
planets or bright stars — for every three hours of Greenwich 
time; and if the astronomer or navigator measures this dis- 
tance with a sextant, he has the means of finding at what 
Greenwich time the distance was equal to that measured. Un- 
fortunately, however, this operation is much like that of deter- 
mining the time from a clock which has nothing but an hour- 
hand. The moon moves among the stars only about 13° in 
a day, and her own diameter in an hour. If the observer wants 
his Greenwich time within half a minute, he must determine 
the position of the moon within the hundred and twentieth of 
her diameter. This is about as near as an ordinary observer 
at sea can come with a sextant ; and yet the error would be \\ 
miles of longitude. Even this degree of exactness can be ob- 
tained only by having the moon's place relatively to the stars 
predicted with great accuracy ; and here we meet with one of 
the most complex problems of astronomy, the efforts to solve 
which have already been mentioned. 

In addition to the uncertainty of which we have spoken, 
this method is open to the objection of being difficult, owing 
to the long calculation necessary to free the measured distance 
from the effects of the refraction of both bodies by the atmos- 
phere, and of the parallax of the moon. On ordinary voyages 
navigators prefer to trust to their chronometers. The error of 
the chronometer on Greenwich time and its daily rate are 
determined at ports of which the longitude is known, and the 
navigator can then calculate this error on the supposition that 
the chronometer gains or loses the same amount every day. 
On voyages between Europe and America a good chronome- 
ter will not generally deviate more than ten or fifteen seconds 
from its calculated rate, so that it answers all the purposes of 
navigation. 

Still another observation by which Greenwich time may be 
obtained to a minute in any part of the world is that of the 
eclipses of Jupiter's first satellite. The Greenwich or Wash- 



164- PRACTICAL ASTRONOMY. 

• 

ington times at which the eclipses are to occur are given in 
the Nautical Almanac, so that if the traveller can succeed in 
observing one, he has his Greenwich time at once, without any 
calculation whatever. But the error of his observation may 
be half a minute, or even an entire minute, so that this meth- 
od is not at all accurate. 

Where an astronomer can fit up a portable observatory, the 
observation of the moon affords him a much more accurate 
longitude than it does the navigator, because he can use better 
instruments. If he has a transit instrument, he determines 
from observation the right ascension of the moon's limb as 
she passes his meridian, and then, referring to the Nautical 
Almanac, he finds at what Greenwich time the limb had this 
right ascension. A single transit would, if the moon's place 
were correctly predicted, give a longitude correct within six 
or eight seconds of time. It is found, however, that, owing to 
the errors of the moon's tables, it is necessary for the astron- 
omer to wait for corresponding observations of the moon at 
some standard observatory before he can be sure of this de- 
gree of accuracy. 

§ 4. Mean, or Clock, Time. 

We have hitherto described only sidereal time, which corre- 
sponds to the diurnal revolution of the starry sphere, or, more 
exactly yet, of the vernal equinox. Such a measure of time 
would not answer the purposes of civil life, and even in astron- 
omy its use is generally confined to the determination of right 
ascensions. Solar time, regulated by the diurnal motion of the 
sun, is almost universally used in astronomical observations as 
well as in civil life. Formerly, solar time was made to con- 
form absolutely to the motion of the sun ; that is, it was noon 
when the sun was on the meridian, and the hours were those 
that would be given by a sundial. If the interval between 
two consecutive transits of the sun were always the same, 
this measure would have been adhered to. But there are two 
sources of variation in the motion of the sun in right ascen- 
sion, the effect of which is to make these intervals unequal : 



MEAN, OR CLOCK, TIME. 165 

1. The eccentricity of the earth's orbit. In consequence 
of this, as already explained, the angular motion of the earth 
round the sun is more rapid in December, when the earth is 
nearest the sun, than in June, when it is farthest. The aver- 
age, or mean, motion is such that the sun is 3 minutes 56 sec- 
onds longer in returning to the meridian than a star is. But, 
owing to the eccentricity, this motion is actually one-thirtieth 
greater in December, and the same amount less in June ; so 
that it varies from 3 minutes 48 seconds to 4 minutes 4 sec- 
onds. 

2. The principal source of the inequality referred to is the 
obliquity of the ecliptic. When the sun is near the equinoxes, 
his motion among the stars is oblique to the direction of the 
diurnal motion; while the latter motion is directly to the 
west, the former is 23£° north or south of east. If, then, sun 
and star cross the meridian together one day near the equinox, 
he will not be 3 minutes 56 seconds later than the star in 
crossing the next day, but about one -twelfth less, or 20 sec- 
onds. Therefore, at the times of the equinoxes, the solar days 
are about 20 seconds shorter than the average. At the sol- 
stices, the opposite effect is produced. The sun, being 23^° 
nearer the pole than before, the diurnal motion is slower, and 
it takes the sun 20 seconds longer than the regular interval of 
3 minutes 56 seconds for that motion to carry the sun over 
the space which separates him from the star which culminat- 
ed with him the day before. The days are then 20 seconds 
longer than the average, from this cause. 

So long as clocks could not be made to keep time within 
20 seconds a day, these variations in the course of the sun 
were not found to cause any serious inconvenience. But 
when clocks began to keep time better than the sun, it be- 
came necessary either to keep putting them ahead when the 
sun went too fast, and behind w T hen he went too slow, or to 
give up the attempt to make them correspond. The latter 
course is now universally adopted, where accurate time is re- 
quired ; the standard sun for time being, not the real sun, but 
a " mean sun," which is sometimes ahead of the real one, and 



166 PRACTICAL ASTRONOMY. 

sometimes behind it. The irregular time depending on the 
motion of the true sun, or that given by a sundial, is called 
Apparent Time, while that given by the mean sun, or by a 
clock going at a uniform rate, is called Mean Time. The two 
measures coincide four times in a year; during two interme- 
diate seasons the mean time is ahead, and during two it is 
behind. The following are the dates of coincidence, and of 
maximum deviation, which vary but slightly from year to 
year : 

February 1 Oth True sun 15 minutes slow. 

April 15th " " correct. 

May 14th " " 4 minutes fast. 

June 14th. " ' ; correct. 

July 25th " " 6 minutes slow. 

August 31st " " correct. 

November 2d " " 16 minutes fast. 

December 24th " " correct. 

When the sun is slow, it passes the meridian after mean noon, 
and the clock is faster than the sundial, and vice versa. These 
wide deviations are the result of the gradual accumulations of 
the deviations of a few seconds from day to day, the cause of 
which has just been explained. Thus, during the interval be- 
tween November 2d and February 12th, the sun is constantly 
falling behind the clock at an average rate of 18 or 19 seconds 
a day, which, continued through 100 days, brings it from 16 
minutes fast to 15 minutes slow. 

This difference between the real and the mean sun is called 
the Equation of Time. One of its effects, which is frequently 
misunderstood, is that the interval from sunrise until noon, as 
given in the almanacs, is not the same as that between noon 
and sunset. This often leads to the inquiry whether the fore- 
noons can be longer or shorter than the afternoons. If by 
" noon " we meant the passage of the real sun across the me- 
ridian, they could not ; but the noon of our clocks being some- 
times 15 minutes before or after noon by the sun, the former 
may be half an hour nearer to sunrise than to sunset, or vice 
versa. 



PARALLAX IN GENERAL, 167 



CHAPTER III. 

MEASURING DISTANCES IN TIIE HEAVENS. 

§ 1. Parallax in General. 

The determination of the distances of the heavenly bodies 
from us is a much more complex problem than merely deter- 
mining their apparent positions on the celestial sphere. The 
latter depend entirely on the direction of the bodies from the 
observer ; and two bodies which lie in the same direction will 
seem to occupy the same position, no matter how much farther 
one may be than the other. Notwithstanding the enormous 
differences between the distances of different heavenly bodies, 
there is no way of telling even which is farthest and which 
nearest by mere inspection, much less can the absolute dis- 
tance be determined in this way. 

The distances of the heavenly bodies are generally deter- 
mined from their Parallax. Parallax may be denned, in the 
most general way, as the difference between the ^ 

directions of a body as seen from two different f*F 

points. Other conditions being equal, the 1^'}^ 

more distant the body, the less this differ- 
ence, or the less the parallax. To show, in // ~ \\ 
the most elementary way, how difference of // \\ 
direction depends on distance, suppose an u \\ 
observer at to see two lights, A and B, at // \> x 
night. He cannot tell by mere inspection j'o p\ 
which is the more distant. But suppose he fh».4T.- Diagiaun Mro- 
walks over to the point P. Both lights will trating P ar * nax - 
then seem to change their direction, moving in the direction 
opposite to that in which he goes. But the light A will change 
more than the light B, for, being to the right of B when the 



168 PRACTICAL ASTRONOMY. 

observer was at 0, it is now to the left of it. The observer 
can then say with entire certainty that A is nearer than B. 

As a steamship crosses the ocean, near objects at rest 
change their direction rapidly, and soon flit by, while more 
distant ones change very slowly. The stars are not seen to 
change at all. If, however, the moon did not move, the pas- 
senger would see her to have changed her apparent position 
about one and a half times her diameter in consequence of 
the journey. If, when the moon is near the meridian, an ob- 
server could in a moment jump from New York to Liverpool, 
keeping his eye fixed upon her, he would see her apparently 
jump in the opposite direction about this amount. 

Astronomically, the direction of an object from an observer 
is determined by its position on the celestial sphere ; that is, 
by its right ascension and declination. In consequence of 
parallax, the declination of a body is not the same when seen 
from different parts of the earth. As the moon passes the 
meridian of the Cape of Good Hope, her measured declina- 
tion may be a degree or more farther north than it is when 
she passes the meridian of Greenwich. The determination of 
the parallax of the moon was one of the objects of the British 
Government in establishing an observatory at the Cape, and 
so well has this object been attained that the best determina- 
tions of the parallax have been made by comparing the Green- 
wich and Cape observations of the moon's declination. 

The determination of the distance of a celestial object from 
the parallax depends on the solution of a triangle. If, in Fig. 
48, we suppose the circle to represent the earth, and imagine 

an observer at A to view a celes- 
tial object, M, he will see it pro- 
jected on the infinite celestial 
sphere in the direction AM con- 
tinued. Another observer at A' 
will see it in the direction A'M. 
The difference of these directions 
is the angle at M. Knowing all 
Fig. 48.— Diagram illustrating parallax, the angles of the quadrilateral 




PARALLAX IX GEXERAL. 



169 




ACA'M, and the length of the earth's radius, CA, the dis- 
tance of the object from the three points, A, A', and C, can 
be found by solving a simple problem of trigonometry. 

The term parallax is frequently used in a more limited 
sense than that in which we have just defined and elucidated 
it. Instead of the difference of directions of a celestial body 
seen from any two points, the astronomer generally means the 
difference between the direction 
of the body as it would appear 
from the centre of the earth, and 
the direction seen by an observer 
at the surface. Thus, in Fig. 49, 
an observer at the centre of the 
earth, C, would see the object M' 
in the direction CAT, while one 
on the surface at P will see it in 
the direction PJf. The differ- 
ence of these directions is the fi... & 
angle PM'C. If the observer 
should be at the point where the line W C intersects the sur- 
face of the earth, there would be no parallax : in this case, 
the object would be in his geocentric zenith. If, on the other 
hand, the observer has the object in his horizon, so that the 
line PM" is tangent to the surface of the earth, the angle 
CJf'P is called the horizontal parallax. The horizontal paral- 
lax is equal to the angle which the radius of the earth subtends as 
seen from the object. When we say that the horizontal parallax 
of trie moon is 57", and that of the sun S".S5, it is the same 
thing as saying that the diameter of the earth subtends twice 
those angles as seen from the moon and sun respectively. 

Owing to the ellipticity of the earth, all its diameters will 
not subtend the same angle ; the polar diameter being the 
shortest of all, and the equatorial the longest. The equatorial 
diameter is, therefore, adopted by astronomers as the standard 
for parallax. The corresponding parallax, that is, the equato- 
rial radius of the earth as seen from a celestial body, is called 
the Equatorial Horizontal Parallax of that body. 



Variation of parallax with the 
altitude. 



170 PRACTICAL ASTRONOMY. 

To measure directly the distance of the moon or any other 
heavenly body, the line PCmust be replaced by the line join- 
ing the positions of the two observers, called the base-line. 
Knowing the length and direction of this base-line, and the 
difference of directions, or parallax, the distance is at once ob- 
tained. If the absolute length of the base-line should not be 
known, the astronomer could still determine the proportion 
of the distance of the object to the base-line, leaving the final 
determination of the absolute distances to be made when the 
base-line could be measured. 

It is not always necessary for two observers actually to sta- 
tion themselves in two distant parts of the earth to determine 
a parallax. If the observer himself could move along the 
base-line, and keep up a series of observations on the object, to 
see how it seemed to move in the opposite direction, he would 
still be able to determine its distance. Now, every observer is 
actually carried along by two such motions, because he is on 
the moving earth. He is carried round the sun every year, 
and round the axis of the earth every day. We have already 
shown how, in consequence of the first motion, all the planets 
seem to describe a series of epicycles. This apparent motion 
is an effect of parallax, and by means of it the proportions of 
the solar system can be determined with extreme accuracy. 
The base-line is the diameter of the earth's orbit. But the 
parallax in question does not help us to determine this base- 
line. To find it, we must first know the distance of the earth 
from the sun, and here we have no base-line but the diameter 
of the earth itself. Nor can the annual motion of the earth 
round the sun enable us to determine the distance of the 
moon, because the latter is carried round by the same motion. 

The result of the daily revolution of the observer round the 
earth's axis is, that the apparent movement of the planet along 
its course is not perfectly uniform : when the observer is east, 
the planet is a little to the west, and vice versa. By observing 
the small inequalities in the motion of the planet correspond- 
ing to the rotation of the earth on its axis, we have the means 
of observing its distance with the earth's diameter as a base- 



PARALLAX IN GENERAL. 171 

line, and this diameter is well known. Unfortunately, how- 
ever, the earth is so small compared with the distances of the 
planets, that the parallax in question almost eludes measure- 
ment, except in the case of those planets which are nearest 
the earth, and even then it is so minute that its accurate de- 
termination is one of the most difficult problems of modern 
astronomy. 

The principal difficulty in determining a parallax from the 
revolution of the observer around the earth's axis is that the 
observations are not to be made in the meridian, but when the 
planet is near the horizon in the east and west. Hence the 
most accurate and convenient instrument of all, the meridian 
circle, cannot be used, and recourse must be had to methods 
of observation subject to many sources of error. 

In measuring very minute parallaxes, it may be doubtful 
whether the position of the body on the celestial sphere can 
be determined with the necessary accuracy. In this case re- 
sort is sometimes had to relative parallax. By this is meant 
the difference between the parallaxes of two bodies lying near- 
ly in the same direction. The most notable example of this 
is afforded by a transit of Venus over the face of the sun. 
To determine the absolute direction of Venus when nearest 
the earth with the accuracy required in measurements of par- 
allax has not hitherto been found practicable, because the ob- 
servation must be made in the daytime, when the atmosphere 
is much disturbed by the rays of the sun, and also because 
only a small part of the planet can then be seen. But if the 
planet is actually between us and the sun, so as to be seen pro- 
jected on the sun's face, the apparent distance of the planet 
from the centre or from the limb of the sun may be found 
with considerable accuracy. Moreover, this distance will be 
different as seen from different parts of the earth's surface at 
the same moment, owing to the effect of parallax ; that is, dif- 
ferent observers will see Venus projected on different parts of 
the sun's face. But the change thus observed will be only 
that due to the difference of the parallaxes of the two bodies; 
while both change their directions, that nearest the observer 



172 PRACTICAL ASTRONOMY. 

changes the more, and thus seems to move past the other, ex- 
actly as in the diagram of the lights. 

It may be asked how the parallax of the sun can be found 
from observations of the transit of Venus, if such observations 
show only the difference between the parallax of Venus and 
that of the sun. We reply that the ratio of the parallaxes of 
the two bodies is known with great precision from the propor- 
tions of the system. We have already shown that these pro- 
portions are known with great accuracy from the third law of 
Kepler, and from the annual parallax produced by the revolu- 
tion of the earth round the sun. It is thus known that at the 
time of the transit of Yenus, in 1874, the sun was nearly four 
times the distance of Yenus, or, more exactly, that he. was 
3.783 times as far as that planet. Consequently, the parallax 
of Yenus was then 3.783 times that of the sun. The differ- 
ence of the parallaxes, that is, the relative parallax, must then 
have been 2.783 times the sun's parallax. Consequently, we 
have only to divide the relative parallax found from the ob- 
servations by 2.783 to have the parallax of the sun itself. 

Still another parallax, seldom applied except to the fixed 
stars, is the Annual Parallax. This is the parallax already ex- 
plained as due to the annual revolution of the earth in its or- 
bit. It is equal to the angle subtended by the line joining the 
earth and sun, as seen from the star or other body. When we 
say that the annual parallax of a star is one second of arc, it is 
the same thing as saying that at the star the line joining the 
earth and sun would subtend an apparent angle of one sec- 
ond, or that the diameter of the earth's orbit would appear un- 
der an angle of two seconds. 

It will be seen that the measurement of the heavens involves 
two separate operations. The one consists in the determina- 
tion of the distance between the earth and the sun, which is 
made to depend on the solar parallax, or the angle which the 
semidiameter of the earth subtends as seen from the sun, and 
which is the unit of distance in celestial measurements. The 
other consists in the determination of the distances of the stars 
and planets in terms of this unit, which gives what we may 



MEAStRES OF THE DISTANCE OF THE 8U2T. 173 

call the proportions of the universe. Knowing this proportion, 
we can determine all the distances of the universe when the 
length of our unit or the distance of the sun is known, but not 
before. The determination of this distance is, therefore, one 
of the capital problems of astronomy, as well as one of the most 
difficult, to the solution of which both ancient and modern as- 
tronomers have devoted many efforts. 

§ 2. Measures of the Distance of the Sun, 

We have already shown, in describing the phases of the 
moon, how Aristarchus attempted to determine the distance 
of the sun by measuring the angle between the sun and the 
moon, when the latter appeared half illuminated. From this 
measure, the sun was supposed to be twenty times as far a> 
the moon; a result which arose solely from the accidental er- 
rors of the observations. 

Another method of attacking the problem was applied by 
Ptolemy, but is probably due to Hipparchus. It rests on a 
very ingenious geometrical construction founded on the prin- 
ciple that the more distant the sun, the narrower will be the 
shadow of the earth at the distance of the moon. The actual 
diameter was determined from an ingenious combination of 
two partial eclipses of the moon, in one of which half of the 
moon was south of the limit of the shadow, while in the other 
three-fourths of her diameter was north of the limit ; that is, 
one fourth of the moon's disk was eclipsed. It was thus found 
that the moon's apparent diameter was 3LJ-', and the appar- 
ent diameter of the shadow 40f '. The former number was 
certainly remarkably near the truth. From this it was con- 
cluded that the sun's parallax was 3' 11", and his distance 1210 
radii of the earth. This result was an entire mistake, arising 
from the uncertainty of any measure of so small an angle. 
Really, the parallax is so minute as to elude all measurement 
with any instrument in which the vision is not assisted by the 
use of a telescope. Yet this result continued to figure in as- 
tronomy through the fourteen centuries during which the '*.!/- 
magest" of Ptolemy was the supreme authority, without, appar- 



174 PRACTICAL ASTRONOMY. 

ently, any astronomer being bold enough to seriously under- 
take its revision. 

Kepler and his contemporaries saw clearly that this distance 
must be far too small ; but all their estimates fell short of the 
truth. Wendell came nearest the truth, as he claimed that 
the parallax could not exceed 15". But the best estimate of 
the seventeenth century was made by Huyghens,* the reason 
why it was the best being that it was not founded on any 
attempt to measure the parallax itself, which was then real- 
ly incapable of measurement, but on the probable magnitude 
of the earth as a planet. The parallax of the sun is, as al- 
ready explained, the apparent semidiameter of the earth as 
seen from the sun. If, then, we can find what size the earth 
would appear if seen from the sun, the problem would at once 
be solved. The apparent magnitudes of the planets, as seen 
from the earth, are found by direct measurement with the 
telescope. The proportions of the solar system being known, 
as already explained, it is very easy to determine the magni- 
tudes of all the planets as seen from the sun, the earth alone 
excepted. The idea of Huyghens was that the earth, being a 
planet, its magnitude would probably be somewhere near that 
of the average of the two planets on each side of it, namely, 
Venus and Mars. So, taking the mean of the diameters of 
Venus and Mars, and supposing this to represent the diameter 
of the earth, he found the angle which the semidiameter of 
the supposed earth would subtend from the sun, which would 
be the solar parallax. 

Although this method may look like a happy mode of 
guessing, it was much more reliable than any which had be- 
fore been applied, for the reason that, in supposing the mag- 
nitude of the earth to be between those of Venus and Mars, 
he was likely to be nearer the truth than any measure of an 
angle entirely invisible to the naked eye would be. And, by 
a lucky accident, Huyghens's estimate was nearer the truth 
than any determinations made previous to the transit of Ve- 

* At the close of his " Systema Saturaium." 



MEASURES OF TEE DISTANCE OF THE SUN. 175 

nus in 1769, his result for the distance of the sun being 25,086 
semidiameters of the earth, or 99 millions of miles. If he 
had used the correct diameters of Yenus and Mars, he would 
have been farther from the truth, because the earth is consid- 
erably larger than the mean of Yenus and Mars — in fact, rath- 
er larger than Yenus herself. But the imperfect telescopes 
used by Huyghens showed the planets larger than they really 
were, so that when he took the mean diameter of these planets 
as they appeared in his telescopes, he just hit the diameter of 
the earth, and reached the true solution of the problem. 

We now come to the modern methods of measuring the 
parallax of the sun. These consist, not in measuring this par- 
allax directly, because this cannot even now be done with any 
accuracy, but in measuring the parallax of one of the planets 
Yenus and Mars when nearest the earth. These planets pass- 
ing from time to time much nearer to us than the sun does, 
have then a much larger parallax, and one which can easily 
be measured. Having the parallax of the planet, that of the 
sun is determined from the known proportion between their 
respective distanoes. 

The first application of this method was made by the French 
astronomers to the planet Mars. In 1671 they sent an ex- 
pedition to the colony of Cayenne, in South America, which 
made observations of the position of Mars during the opposi- 
tion of 1672, while corresponding observations were made at 
the Paris Observatory. The difference of the two apparent 
positions, reduced to the same moment, gave the parallax of 
Mars. From a discussion of these observations, Cassini con- 
cluded the parallax of the sun to be 9".5, corresponding to a 
distance of the sun equal to 21,600 semidiameters of the earth. 
This distance was as much too small as Huyghens's was too 
great, so that, as we now know, no real improvement was 
made. Still, the data were mnch more certain than those on 
which the estimate of Huyghens was made, and for a hundred 
years it was generally considered that the sun's parallax was 
about 10", and his distance between 80 and 90 millions of miles. 

The method bv observations of Mars is still, in some of its 

13 



176 PRACTICAL ASTRONOMY. 

forms, among the most valuable which have been applied to 
the determination of the solar parallax. About once in six- 
teen years Mars approaches almost as near the earth as Yenus 
does at the times of her transits, the favorable times being 
those when Mars at opposition is near his perihelion. His 
distance outside the earth's orbit is then only 0.373 of the as- 
tronomical unit, or 34J millions of miles, while at his aphe- 
lion the distance is nearly twice as great. At the nearest op- 
positions, his parallax is over 23", an angle which can be meas- 
ured with some accuracy. The plan of observation has gen- 
erally been to send an observing party to the southern hemi- 
sphere in advance, for the purpose of making observations of 
the position of Mars on the celestial sphere, or of its distance 
from certain selected stars, from night to night, while corre- 
sponding observations are made at the fixed observatories of 
the northern hemisphere. The displacement of the planet 
due to parallax is then found by comparing the results of 
these observations. 

The last expedition of this sort was that of Captain James 
M. Gilliss, late of the United States Navy, who went out to 
Chili under the auspices of the American Government in 
1849, and remained till 1852, for the purpose of observing 
both Yenus and Mars during the periods when' the parallax 
was greatest. Several circumstances conspired to prevent this 
enterprise from producing results corresponding to its merits. 
The opposition of Mars was a very unfavorable one ; observa- 
tions of Yenus could not be made with the necessary accu- 
racy, and there was a lack of sufficient cooperation on the 
part of northern observers. The astronomical results of the 
expedition were, nevertheless, important, Captain Gilliss hav- 
ing prepared an immense catalogue of the stars of the south- 
ern hemisphere, while his instruments became the property of 
the Government of Chili, which employed them in fitting up 
a national observatory. Several observatories have since been 
founded in the southern hemisphere, so that there is no longer 
any need of sending out expeditions to observe the planet 
Mars for the purpose in question. 



SOLAR PARALLAX FROM TRAXSITS OF VEXUS. 



177 



§ 3. Solar Parallax from Transits of Venus. 

The most celebrated method of determining the solar paral- 
lax has been by transits of Venus over the face of the sun, by 
which the difference between the parallax of the planet and 
that of the sun can be found, as explained in § 1. We know 
from our astronomical tables that this phenomenon has recur- 
red in a certain regular cycle four times every 243 years for 
many centuries past. This cycle is made up of four intervals, 
the lengths of which are, in regular order, 105£ years, 8 years, 
121£ years, 8 years, after which the intervals repeat them- 
selves. The dates of occurrence for eight centuries are as 
follows : 



1518 June 2d. 

1526 June 1st. 

1631 December 7th. 

1630 December 4th. 

1761 June 5th. 

176!) June 3d. 

1874 December 9th. 



1882 December 6th. 

200+ June 8th. 

2012 June 6th. 

2117 December 1 1th. 

2125 -. December 8th. 

2247 June 11th. 

2255 June 9th. 



It has been only in comparatively recent times that this phe- 
nomenon could be predicted and observed. In the years 1518 
and 1526 the idea of looking for such a thing does not seem 
to have occurred to any one. The following century gave 
birth to Kepler, who so far improved the planetary tables 
as to predict that a transit would occur on December 6th, 
1631. But it did not commence until after sunset in Eu- 
rope, and was over before sunrise next morning, so that it 
passed entirely unobserved. Unfortunately, the tables were 
so far from accurate that they failed to indicate the transit 
which occurred eight years later, and led Kepler to announce 
that the phenomenon would not recur till 1761. The transit 
of 1639 would, therefore, like all former ones, have passed 
entirely unobserved, had it not been for the talent and enthu- 
siasm of a young Englishman. Jeremiah Horrox was then a 
young curate of eighteen, residing in the North of England, 
who, even at that early age, was a master of the astronomy of 



178 PRACTICAL ASTRONOMY. 

his times. Comparing different tables with his own observa- 
tions of Venus, he found that a transit might be expected to 
occur on December 4th, and prepared to observe it, after the 
fashion then in vogue, by letting the image of the sun passing 
through his telescope fall on a screen behind it: Unfortu- 
nately, the day was Sunday, and his clerical duties prevented 
his seeing the ingress of the planet upon the solar disk — a cir- 
cumstance which science has mourned for a century past, and 
will have reason to mourn for a century to come. When he 
returned from church, he was overjoyed to see the planet upon 
the face of the sun, but, after following it half an hour, the ap- 
proach of sunset compelled him to suspend his observations. 

During the interval between this and the next transit, which 
occurred in 1761, exact astronomy made very rapid progress, 
through the discovery of the law of gravitation and the ap- 
plication of the telescope to celestial measurements. A great 
additional interest was lent to the phenomenon by Halley's 
discovery that observations of it made from distant points of 
the earth could be used to determine the distance of the sun. 
• The principles by which the parallaxes, and therefore the 
distances, of Yenus and the sun are determined by Halley's 
method are quite simple. In consequence of the parallax of 
Yenus, two observers at distant points of the earth's surface, 

watching her course over the 
solar disk, will see her describe 
slightly different paths, as shown 
in Fig. 50. It is by the distance 
between these paths that the par- 
allax has hitherto been deter- 
mined. 

The essential principle of Hal- 
ley's method consists in the mode 
fig. 50. -Apparent paths of Venus across of determining the distance be- 

the sun, as seen from different stations tween these apparent paths. An 

during the transit of 1874. The upper . „ . « .-,•, ■, 

path is that seen from a southern sta- inspection 01 the ILgUre Will ShOW 

tion; the lower is that seen from a that fa -^ f art h e st from the 
northern station, but the distance be- r 

tween the paths is exaggerated. sun's centre is shorter than the 




SOLAR PARALLAX FROM TRANSITS OF VENUS. 179 

other, so that Venus will pass over the sun more quickly when 
watched from a southern station than when watched from a 
northern one. Halley therefore proposed that the different ob- 
servers should, with a telescope and a chronometer, note the 
time it took Venus to pass over the disk, and the difference be- 
tween these times, as seen from different stations, would give 
the means of determining the difference between the parallaxes 
of Venus and the sun. The ratio between the distances of 
the planet and the sun is known with great exactness by Kep- 
ler's third law, from which, knowing the differences of paral- 
laxes, the distance of each body can be determined. 

By this plan of Halley the observer must note with great 
exactness the times both of beginning and end of the transit 
There are two phases which may be observed at the beginning 
and two at the end, making four in all. 

The first is that when the planet first touches the edge of 
the solar disk, and begins to make a notch in it, as at a, Fig. 50. 
This is called first external contact. 

The second is that when the planet has just entered entirely 
upon the sun, as at b. This is called first internal contact. 

The third contact is that in which the planet, after crossing 
the sun, h'rst reaches the edge of the disk, and begins to go 
off, as at c. This is called second internal contact. 

The fourth contact is that in which the planet finally disap- 
pears from the face of the sun, as at d. This is called second 
external contact. 

Now, it was the opinion of Halley, and a very plausible one, 
too, that the internal contacts could be observed with far great- 
er accuracy than the external ones. He founded this opinion 
on his own experience in observing a transit of the planet Mer- 
cury at St. Helena in 1677. It will be seen by inspecting Fig. 
51, which represents the position of the planet just before first 
internal contact, that as the planet moves forward on the solar 
disk the sharp horns of light on each side of it approach each 
other, and that the moment of internal contact is marked by 
these horns meeting each other, and forming a thread of light 
all the way across the dark space, as in Fig. 52. This thread 




ISO PRACTICAL ASTRONOMY. 

of light is indeed simply the extreme edge of the sun's disk 
coming into view behind the planet. In observing the tran- 
sit of Mercury, Halley felt 
sure that he could fix the 
moment at which the horns 
met, and the edge of the 
sun's disk appeared un- 
broken, within a single sec- 
ond; and he hence con- 
cluded that observers of 
the transit of Venus could 
observe the time required 

Fig. 51.— Venus approaching internal contact on 10 r VenUS to paSS aCl'OSS 
the face of the sun. The planet is supposed fa Q glm w j t hin One Or tWO 
to be moving upward. 

seconds. These times would 
differ in different parts of the earth by fifteen or twenty min- 
utes, in consequence of parallax. Hence it followed, that if 
Halley 's estimate of the de- 
gree of accuracy attainable 
were correct, the parallax of 
Yen us and the sun would be 
determined by the proposed 
system of observations within 
the six hundredth of its whole 
amount. 

When the long-expected 5th 
of June, 1761, at length ap- 
proached, which was a gener- 
ation after Halley's death, ex- FlG - ^—Internal contact of the limb of Ve- 
J 3 nus with that of the sun. 

peditions were sent to distant 

parts of the world by the principal European nations to make 
the required observations. The French sent out from among 
their astronomers, Le Gentil to Pondicherry ; Pingre to Rod- 
riguez Island, in the neighborhood of the Mauritius ; and the 
Abbe Chappe to Tobolsk, in Siberia. The war with England, 
unfortunately, prevented the first two from reaching their sta- 
tions in time, but Chappe was successful. From England, Ma- 




SOLAR PARALLAX FROM TRANSITS OF. VENUS. 



181 



son — he of the celebrated Mason and Dixon's Line — was sent 
to Sumatra ; but he, too, was stopped by the war : Maskelyne, 
the Astronomer Royal, was sent to St. Helena. Denmark, 
Sweden, and Russia also sent out expeditions to various points 
in Europe and Asia. 

With those observers who were favored by fine weather, the 
entry of the dark body of Venus upon the limb of the sun 
was seen very well until the critical moment of internal con- 
tact approached; Then they were perplexed to find that the 
planet, instead of preserving its circular form, appeared to 
assume the shape of a pear or a balloon, the elongated portion 
being connected with the limb of the sun. We give two fig- 
ures, 52 and 53, the first showing how the planet ought to have 
looked, the last how it really did look. Now, we can readily 
see that the observer, looking 
at such an appearance as hi 
Fig. 53, would be unable to 
say whether internal contact 
had or had not taken place. 
The round part of the planet 
is entirely within the sun, so 
that if he judged from this 
alone, he would say that in- 
ternal contact is passed. But 
the horns are still separated 
by this dark elongation, or 
" black drop," as it is general- 
ly called, so that, judging from this, internal contact has not 
taken place. The result was an uncertainty sometimes amount- 
ing to nearly a minute in observations which were expected to 
be correct within a single second. 

When the parties returned home, and their observations 
were computed by various astronomers, the resulting values 
of the solar parallax were found to range from 8".5, found by 
Short of England, to 10".5, found by Pingre, of France, so 
that there was nearly as much uncertainty as ever in the value 
of the element sought. Nothing daunted, however, prepara- 




Fig. 53.— The black drop, or ligament. 



182 PEACTICAL ASTRONOMY. 

tions yet more extensive were made to observe the transit of 
1769. Among the observers was one whose patience and 
whose fortune must excite our warmest sympathies. We have 
said that Le Gentil, sent out by the French Academy to ob- 
serve the transit of 1761 in the East Indies, was prevented 
from reaching his station by the war with England. Finding 
the first port he attempted to reach in the possession of the 
English, his commander attempted to make another, and, 
meeting with unfavorable winds, was still at sea on the day of 
the transit. He thereupon formed the resolution of remain- 
ing, with his instruments, to observe the transit of 1769. He 
was enabled to support himself by some successful mercantile 
adventures, and he also industriously devoted himself to scien- 
tific observations and inquiries. The long-looked-for morning 
of June 4th, 1769, found him thoroughly prepared to make 
the observations for which he had waited eight long years. 
The sun shone out in a cloudless sky, as it had shone for a 
number of days previously. But just as it was time for the 
transit to begin, a sudden storm arose, and the sky became 
covered with clouds. When they cleared away the transit 
was over. It was two weeks before the ill-fated astronomer 
could hold the pen which was to tell his friends in Paris the 
story of his disappointment. 

In this transit the ingress of Yenus on the limb of the sun 
occurred just before the sun was setting in Western Europe, 
which allowed numbers of observations of the first two phases 
to be made in England and France. The commencement was 
also visible in this country — which was then these colonies — 
under very favorable circumstances, and it was well observed 
by the few astronomers we then had. The leader among 
these was the talented and enthusiastic Rittenhouse, who was 
already well known for his industry as an observer. The ob- 
servations were organized under the auspices of the American 
Philosophical Society, then in the vigor of its youth, and par- 
ties of observers were stationed at Norristown, Philadelphia, 
and Cape Henlopen. These observations have every appear- 
ance of being among the most accurate made on the transit; 



^^^M 



SOLAR PARALLAX FROM TRANSITS OF VENUS. 1 S3 

but they have not received the consideration to which they are 
entitled, partly, we suppose, because the altitude of the sun 
was too great to admit of their being of much value for the 
determination of parallax, and partly because they were not 
\ery accordant with the European observat' 

The phenomena of the distortion of the planet and the 
"black drop,'* already described, were noticed in this, as in 
the preceding transit. It is strongly indicative of the ill 
preparation of the observers that it seems to have taken them 
all by surprise, except the few who had observed the pre< 
ing transit. The cause of the appearance was first pointed 
out by Lalande, and is briefly this: when we look at a bright 
object on a dark ground, it looks a little larger than it real- 
ly is, owing to the encroachment of the light upon the dark 
border. This encroachment, or irradiation, may arise from a 
number of causes — imperfections of the eye, imperfections of 
the lenses of the telescope when an instrument is used, and 
the softening effect of the atmosphere when we look at a ce- 
lestial object near the horizon. To understand its effect, we 
have only to imagine a false edge painted in white around the 
borders of the bright object, the edge becoming narrower ami 
darker where the bright object is reduced to a very narrow 
line. Thus, by painting around the borders of the light por- 
tions of Fig. 51, we have formed Fig. 53, and produced an ap- 
pearance quite similar to that described by the observers of 
the transit. The better the telescope and the steadier the at- 
mosphere, the narrower this border will be. and the more the 
planet will seem to preserve its true form, as in Fig. 52. In 
the observations of the recent transit of Venus with the im- 
proved instruments of the present time, very few of the more 
experienced observers noticed any distortion at all. 

The results of the observations of 1769 were much more 
accordant than those of 1761. and seemed to indicate a paral- 
lax of about S".5. Curious as it may seem, more than half a 
century elapsed after the transit before its results were com- 
pletely worked up from all the observations in an entirely 
satisfactory manner. This was at length done by Encke, in 



184 PRACTICAL ASTRONOMY. 

1824, for both transits, the result giving 8".5776 for the solar 
parallax. Some suspicion, however, attached to some of the 
observations, which he was not at that time able to remove. 
In 1835, having examined the original records of the observa- 
tions in question, he corrected his work, and found the follow- 
ing separate results from the two transits : 

Parallax from the observations of 1761... 8". 53 

Parallax from the observations of 1769 8". 59 

Most probable result from both transits 8".571 

The probable error of the result was estimated at 0".037, 
which, though larger than was expected, was much less than 
the actual error has since proved to be. The corresponding 
distance of the sun is 95,370,000 miles, a classic number 
adopted by astronomers everywhere, and familiar to every 
one who has read any work on astronomy. 

This result of Encke was received without question for 
more than thirty years. But in 1854 the celebrated Hansen, 
completing his investigations of the motions of the moon, 
found that her observed positions near her first and last quar- 
ters could not be accounted for except by supposing the par- 
allax of the sun increased, and therefore his distance dimin- 
ished, by about a thirtieth of its entire amount. The exist- 
ence of this error has since been amply confirmed in several 
ways. The fact is, that although a century ago a transit of 
Yen us afforded the most accurate way of obtaining the dis- 
tance of the sun, yet the great advances made during the 
present generation in the art of observing, and the applica- 
tion of scientific methods, have led to other means of greater 
accuracy than these old observations. It is remarkable that 
while nearly every class of observations is now made with 
a precision which the astronomers of a century ago never 
thought possible, yet this particular observation of the interior 
contact of a planet with the limb of the sun has never been 
made with any thing like the accuracy which Halley himself 
thought he attained in his observation of the transit of Mer- 
cury two centuries ago. 



SOLAR PARALLAX FROM TRANSITS OF VENUS. 185 

The knowledge of this error in the fundamental astronom- 
ical unit gave increased interest to the transit of Venus which 
was to occur on December 8th, 1874. The rarity of the phe- 
nomenon was an advantage, in that it led to an amount of 
public interest being taken in it which could not have been 
excited by any other astronomical event, and thus secured 
from various governments the grants necessary to fit out the 
necessary parties of observation. Plans of observation began 
to be worked out very far in advance. In 1857, Professor 
Airy sketched a general plan of operations for the observation 
of the transits, and indicated the regions of the globe in which 
he considered the observations should be made. In 1870, be- 
fore any steps whatever were taken in this country, he had ad- 
vanced so far in his preparations as to have his observing huts 
all ready, and his instruments in process of construction. In 
18G9, the Prussian Government appointed a commission, con- 
sisting of six or eight of its most eminent astronomers, to de- 
vise a plan of operations, and report it to the Government 
with an estimate of the expenses. About the same time the 
Kussian Government began making extensive preparations 
for observing the transit from a great number of stations in 
Siberia. 

Active preparations for the observations in question were 
commenced by the United States Government in IS 71. An 
account of the method of observation adopted by the Com- 
mission to whom the matter was intrusted may not be devoid 
of interest. The observations of the older transits having 
failed in giving results of the accuracy now required, it be- 
came necessary to improve upon the system then adopted. 
In this system, the parallax depended entirely on observations 
of contacts, the uncertainty of which we have already shown. 
Besides this uncertainty, Halley's method was open to the ob- 
jection that, unless both contacts were observed at each sta- 
tion, the path of Venus could not be determined, and no re- 
sult could be deduced. It was therefore proposed by De 
Flsle early in the last century, that the observers should de- 
termine the longitudes of their stations, in order that, by 



136 PRACTICAL ASTRONOMY. 

means of it, they could find the actual intervals between the 
moments at which any given contact was seen at the different 
stations. This method was an improvement on Halley's, in 
that it diminished the chances of total failure. Still, it de- 
pended entirely upon making an accurate observation of the 
moment of contact, and was liable to fail from any accident 
which might interfere with such an observation — a passing 
cloud, or a disarrangement of some of the instruments of ob- 
servation. Besides, it was not yet certain whether the obser- 
vations could be made with the necessary accuracy. It was, 
therefore, desirable that, instead of depending on contacts 
alone, some method should be adopted of finding the position 
of Venus on the face of the sun as often as possible during 
the four hours which she should occupy in passing. The 
easiest and most effective way of doing this seemed to be to 
take photographs of the sun with Venus on his disk, which 
photographs could be brought home, compared, and measured 
at leisure. 

This mode of astronomical measurement has been brought 
to great perfection in this country by Mr. L. M. Eutherfurd 
and others, and has been found to give results exceeding in 
accuracy any yet attained by ordinary eye observations. The 
advantages of the photographic method are so obvious that 
there could be no hesitation about employing it, and, so far 
as is known, it was applied by every European nation which 
sent out parties of observation. But there is a great and 
essential difference between the methods of photographing 
adopted by the Americans and by most of the Europeans. 
The latter seem to have devoted all their attention to the 
problem of securing a good sharp photograph, taking it for 
granted that when this photograph was measured there would 
be no further difficulty. But the measurement at home is 
necessarily made in inches and fractions, wiiile the distance 
we must know is to be found in minutes and seconds of an- 
gular measure. If we have a map by measurements on which 
we desire to know the exact distance of two places, we must 
first know the exact scale on which the map is laid down, 



SOLAR PARALLAX FROM TRANSITS OF VENUS. 187 

with a degree of accuracy corresponding to that of our meas- 
ures. Just so with our photographs taken at various parts of 
the globe. We must know the scale on which the images are 
photographed before we can derive any conclusions from our 
measures. While the determination of this scale with suffi- 
cient precision for ordinary purposes is quite easy, this is by 
no means the case with a problem where so much accuracy 
was required, so that here lay the greatest difficulty which the 
photographic method offered. 

In the mode of photographing adopted by the Americans 
this difficulty was met by using a telescope of great length 
— nearly forty feet. So long a telescope would be too un- 
wieldy to point at the sun ; it was therefore fixed in a hor- 
izontal position, the rays of the sun being thrown into it by a 
mirror. The scale of the picture was determined by actually 
measuring the distance between the object-glass and the pho- 
tograph-plate. Each station was supplied with special appa- 
ratus by which this measurement could be made within the 
hundredth of an inch. Then, knowing the position of the op- 
tical centre of the glass, it is easy to calculate exactly how 
many inches any given angle will subtend on the photograph- 
plate. The following brief description of the apparatus will 
be readily understood by reference to the figures : 

The object-glass and the support for the mirror are mount- 
ed on an iron pier extending four feet into the ground, and 
firmly embedded in concrete. The mirror is in a frame at 
the end of an inclined cast-iron axis, which is turned with a 
very slow motion by a simple and ingenious piece of clock- 
work. The inclination of the axis and the rate of motion are 
so adjusted that, notwithstanding the diurnal motion of the 
sun — or, to speak more accurately, of the earth — the sun's 
rays will always be reflected in the same direction. This re- 
sult is not attained with entire exactness, but it is so near that 
it will only be necessary for an assistant to touch the screws 
of the mirror at intervals of fifteen or twenty minutes during 
the critical hours of the transit. The reflector is simply a 
piece of finely polished glass, without any silvering whatever. 



188 



PRACTICAL ASTRONOMY. 



It only reflects about a twentieth of the sun's light ; but so in- 
tense are his rays that a photograph can be taken in less than 
the tenth of a second. The polishing of this mirror was the 
most delicate and difficult operation in the construction of 
the apparatus, as the slightest deviation from perfect flatness 
would be fatal. For instance, if a straight edge laid upon the 
glass should touch at the edges, but be the hundred- thou- 
sandth of an inch above it at the centre, the reflector would 
be useless. It might have seemed hopeless to seek for such a 
degree of accuracy, had it not been for the confidence of the 
Commission in the mechanical genius of Alvan Clark & Sons, 
to whom the manufacture of the apparatus was intrusted. 
The mirrors were tested by observing objects through a tele- 
scope, first directly, and then by reflection from the mirror. 
If they were seen with equally good definition in the two 
cases, it would show that there were no irregularities in the 
surface of the mirror; while if it were either concave or con- 
vex, the focus of the telescope would seem shortened or 
lengthened. The first test was sustained perfectly, while the 




39'-' AND A FBACTIOM. 5=- 




Fig. 54 — Method of photographing the transit of Venns used hy the French and Ameri- 
can observers, and by Lord Lindsay. 



SOLAR PARALLAX FROM TRANSITS OF VENUS. 189 

circles of convexity or concavity indicated by the changes of 
focus of the photographic telescope were many miles in di- 
ameter. 

Immediately in front of the mirror is the object-glass. The 
curves of the lenses of which it is formed are so arranged that 
it is not perfectly achromatic for the visual rays, but gives the 
best photographic image. Thirty -eight feet and a fraction 
from the glass is the focus, where an image of the sun about 
four and a quarter inches in diameter is formed. Here an- 
other iron pier is firmly embedded in the ground for the sup- 
port of the photographic plate - holder. This consists of a 
brass frame seven inches square on the inside, revolving on a 
vertical rod, which passes through the iron plate on top of the 
pier. Into this frame is cemented a square of plate-glass, just 
as a pane of glass is puttied in a window. The glass is divided 
into small squares by very fine lines about one-five-hundredth 
of an inch thick, which were etched by a process invented and 
perfected by Mr. W. A. Rogers, of the Cambridge Observatory. 
The sensitive plate goes into the other side of the frame, and 
when in position for taking the photograph, there is a space 
of about one-eighth of an inch between the ruled lines and 
the plate. The former are, therefore, photographed on every 
picture of the sun which is taken, and serve to detect any 
contraction of the collodion film on the glass plate. 

The rod on which the plate-holder turns, and the frame it- 
self, are perforated from top to bottom by a vertical opening 
one-sixth of an inch in diameter. Through the centre of this 
opening, passing between the ruled plate and the photograph 
plate, hangs a plumb-line of very fine silver wire. In every 
picture of the sun this plumb-line is also photographed, and 
this marks a truly vertical line on the plate very near the mid- 
dle vertical etched line. A spirit-level is fixed to the top of 
the frame, and serves to detect any changes in the inclination 
of the ruled lines to the horizon. 

One of the most essential features of the arrangement is 
that the photographic object-glass and plate-holder are on the 
same level, and in the meridian of the transit instrument with 



190 PRACTICAL ASTRONOMY. 

which the time is determined. The central ruled line on the 
plate-holder is thus used as a meridian mark for the transit. 
The great advantage of this arrangement is, that it permits 
the angle which the line joining the centres of the sun and 
Venus makes with the meridian to be determined with the 
greatest precision by means of the image of the plumb-line 
which is photographed across the picture of the sun.* 

Although the contact observations were not wholly relied 
on, they were by no means neglected. On the contrary, the 
greatest pains were taken to avoid the sources of error which 
caused so much trouble in 1769. To learn what these errors 
probably were, and to practise the observers in making their 
observations so as to avoid them, an artificial planet was con- 
structed to move over an artificial representation of a portion 
of the solar disk by clock-work. The apparatus was mounted 
on the top of a building about 3300 feet distant, in order to 
give the effect of atmospheric undulations and softening of 
the edges of the planet. The planet was represented by a 
black disk one foot in diameter, which made its apparent mag- 
nitude the same as that 
of Venus in transit. The 
sun was represented by 
a white screen behind 
the artificial Venus, the 
portions of the edge of 

Fi«.55.-Artiflcial transit of Venus. ^ digk where y Qm ^ 

entered and left being formed by the sloping edges of a black 
triangle, as shown in the figure. There was no need of a rep- 
resentation of the entire sun. The motion was so regulated 
that the time occupied by the disk in passing from external to 

* The method of photographing the sun by a fixed horizontal telescope with a 
reflector in front of it is believed to have been first proposed in France by Captain 
Laussedat. It was independently invented by the late Professor Winlock, who 
put it into actual operation at the Harvard College Observatory in 1869, and, so 
far as the author is aware, was the first one to do so. It was employed not only 
by the American observers, but by the French, and by Lord Lindsay, M.P., of 
Scotland. The latter gentleman fitted out a finely equipped expedition at his own 
expense to observe the transit of Venus at the Mauritius. 



■L/XCHV/ii. UlOIl \JL1\J JLWU J.i-1 UiaillC/lDl. VV IIAVjAJ 

09 



SOLAR PARALLAX FROM TRANSITS OF VENUS. 191 

internal contact, and the angle its motion made with the edges 
of the triangle, were the same as they would be in the actual 
transit as viewed from some point where it occurred near the 
zenith. The disk was put at such a height that it was only 
about thrje minutes from internal contact at ingress to inter- 
nal contact at egress, instead of four hours. 

The observations of this instrument have thrown much light 
on the question of the black drop, and the distortion of the 
planet seen in former transits of Venus, which have been al- 
ready described. What is perhaps yet better, it lias enabled 
us to account for a number of puzzling and discordant appear- 
ances described by the observers. Father Hell's black drop, 
seen before the limbs were in contact ; the formation of inter- 
nal contact by a fine line of light, though the cusps were blunt, 
as seen at Hudson Bay ; Captain Cook's "atmosphere'' around 
Venus, and his curious black piece cut out of the edge of the 
sun, may all be said to have been identified nearly enough to 
judge what the appearances really were which were so vari- 
ously described. In looking at the artificial planet near the 
moment of internal contact, when the air is not still, the first 
tiring which the observer sees is that there is reallv no con- 
stant shape to those parts of Venus and the sun which are ap- 
proaching each other; but that, owing to the undulations of 
the air, they assume all sorts of shapes in rapid succession, so 
that different observers may give different descriptions of the 
appearances presented, though looking at the very same ob- 
ject. In the varied forms which may be seen, we recognize 
all the peculiar appearances described by the observers of the 
transit of 1769. 

At each American station the scientific corps consisted of 
a chief of party, an assistant astronomer, and three photog- 
raphers. The instruments at all the stations were precisely 
similar, and the operations and observations the same at all. 
This system was adopted to secure two great advantages : first. 
to run the least risk of entire failure from bad weather ; and. 
second, to have all the observations strictly comparable. Much 
pains and trouble were devoted to these objects. To appreci- 

U 



192 PRACTICAL ASTRONOMY. 

ate their importance, we must remember that, in order to de- 
duce the parallax from the observations at any two stations, 
it is essential that the difference between observations should 
be due only to parallax, and that in every other respect they 
should be exactly the same ; because, if there are other dif- 
ferences which we cannot certainly allow for, our calculation 
of the parallax will be wrong. It is also necessary that we 
compare the same kind of observations in order to get the 
parallax. To show how the chances of failure are lessened, 
suppose we have two stations in each hemisphere, in one of 
which eye observations are made, while in the other photo- 
graphs are taken. Then, if the photographs in one hemi- 
sphere and the eye observations in the other are lost by clouds, 
or any other cause, everything will be lost, although one sta- 
tion in each hemisphere is successful, because the eye obser- 
vations in the one hemisphere cannot be compared with the 
photographs in the other. It being decided, for these reasons, 
to have the same system of observations at all the stations, it 
became necessary to confine the choice of stations to points 
where the entire transit would be visible. 

One of the most important features of the preparations, 
which distinguishes them from the preparations to observe 
the former transits, was the previous training of the observers. 
All the members of the observing parties assembled at Wash- 
ington to practise together before leaving to make the obser- 
vations. They took all their multitudinous instruments and 
apparatus out of their boxes, mounted them, and proceeded to 
practise with them in the same way they were to be used at 
the stations. Photographs of the sun were taken from day to 
day in the same way as on the 8th of December, and each 
chief of party was instructed in all the delicate operations 
necessary to secure the entire success of his operations. 

To know where a party could be sent, it had first to be 
known when and where the transit would be visible. We 
give a small map of the world showing this at a glance. 
Could we have seen the planet Yenus from the Eastern States 
on the afternoon of December 8th, 1874, we should have seen 



SOLAR PARALLAX FROM TRANSITS OF VENUS. 



193 




Fig. 56.— Map of the earth, showing the areas of visibility of the transit of 1^74. 

her approaching nearer and nearer the sun as the latter ap- 
proached the horizon. In San Francisco, where sunset is three 
hours later than here, she would have been so near the sun as 
almost to seem to touch it. About an hour later she actual- 
ly reached the solar disk. The sun was then shining on the 
whole Pacific Ocean, except that portion nearest the Ameri- 
can coast, and on Eastern Asia, Australia, and the Indian and 
Antarctic oceans to the south pole. Venus was about four 
and a half hours passing over the face of the sun, and during 
this time the latter had set across the entire northern portion 
of the Pacific Ocean, and had risen as far west as Moscow 
and Vienna, from which cities the planet might have been 
seen to leave the disk just as the sun rose. 

In the northern hemisphere suitable stations were easily 
found, as we have the whole of China, Japan, and Northern 
India. But in the southern hemisphere great difficulties were 
encountered, owing to the want of habitable stations in the 
regions which were astronomically the most favorable. Ob- 
servations cannot be made from the deck of a ship ; astrono- 
mers must have solid ground for their instruments. The south 
pole would have been the best station of all, if some antarc- 
tic Kane or Hall could take a party thither. The antarctic 
continent and the neighboring islands were not to be thought 
of, because a party could neither be landed nor subsisted there : 



194 PBACTICAL ASTRONOMY. 

and if they could, the weather would probably have prevented 
any observations from being taken. The chance of having a 
clear sky on the eventful 8th of December was, indeed, one 
of the most important considerations on which the choice of 
a station had to depend. Information from every available 
source, official and private, respecting the meteorology of the 
various possible stations, was therefore sought. Where there 
was any American consul or consular agent, he was applied 
to through the State Department* to have meteorological ob- 
servations made during the months of November and Decem- 
ber, 1872 and 1873. A sealing ship belonging to the firm of 
Williams, Haven, & Co., of New London, made observations 
at Heard's Island, in the Southern Indian Ocean. From all 
these reports, as well as from the printed reports issued by 
various authorities, it was found that the chances of good 
weather were much better in the northern than in the south- 
ern hemisphere. In consequence, instead of sending an equal 
number of parties north and south, it was determined to send 
three to the northern and five to the southern hemisphere. 

The stations which the American parties finally occupied, 
with the names of the chiefs of party, are as follows : 

Northern Hemisphere. 

Wladiwostok, Siberia Professor Asaph Hall, U. S.N. 

Pekin, China Professor J. C. Watson. 

Nagasaki, Japan Professor George Davidson, U. S. Coast Survey. 

Southern Stations. 

Kerguelen Island Commander G. P. Eyan, U. S. N. 

Hobart-town, Tasmania Professor W. Harkness, U. S. N. 

Campbelltown, Tasmania* Captain C. W. Eatmond, Engineer Corps, U. S. A. 

Queenstown, New Zealand. ...Professor C. H. F. Peters. 

Chatham Island Edwin Smith, Esq., U. S. Coast Survey. 

The southern parties were all carried to their respective sta- 
tions by the U. S. steamer Swatara, Captain Ealph Chandler, 
U. S. N., commanding. 



* Captain Eaymond's party was designed for the Crozet Islands, but the Swa- 
tara failed to effect a landing there. 



SOLAR PARALLAX FROM TRANSITS OF VENUS. 195 

The only thing which seriously interfered with the observa- 
tions was the weather. Some photographs were obtained at 
every station, but the full number at none. Altogether, there 
were only about half the expected number obtained. Xo 
contacts at all were observed at Uobart-town or Chatham Isl- 
and, but one or more were observed at each of the remaining 
six stations. Pekin was, however, the only one at which all 
four were observed. Among the parties sent out by other 
nations, the most fortunate, as regards weather, were the Ger- 
mans, who were successful at all six of their stations. The 
English, French, and Russians were, on the average, about as 
successful as the Americans. 

The work of reducing the observations of a transit of Venus 
with all the precision required by modern astronomy is one 
involving an immense mass of calculations, and much tedious 
investigation. Before the final result can be attained, it is 
necessary that all the observations made under the auspices of 
the several governments which took part in the work shall be 
reduced and published, and, after this is done, that sonic one 
shall combine them all, so as to obtain the most probable re- 
sult. Partial results, founded upon a portion of the observa- 
tions, may, indeed, be deduced without waiting for all the 
material ; but the majority of the leading astronomers con- 
ceive that these results will not have any scientific interest : 
and at a meeting of the International Astronomical Society 
(the Astronomische Gesellschaft), held at Leyden, it was voted 
that their publication should be discouraged as injurious to 
science. This view has not, however, been universally ac- 
cepted, and three values of the solar parallax from the obser- 
vations of the transit of 1ST4 have already appeared, one from 
the French, and two from the English observations. 

The French observations here referred to were those made 
at two stations, Peking and St. Paul's Island. They were cal- 
culated by M. Puiseux, a member of the French Academy of 
Sciences, in 1S75, and led to 8".88 as the value of the solar 
parallax. 

The British observations of contacts were worked up, under 



196 PRACTICAL ASTRONOMY. 

the direction of Sir George Airy, in 1877, and were found to 
lead to the surprisingly small result. 8". 76. But Mr. E. J. 
Stone took the very same observations, and, by treating and 
interpreting them in a different way, obtained the result 8".88. 
That two results so different could be obtained from the same 
observations must cast doubt upon their value, and raise ques- 
tions which can be decided only by the combination of all the 
observations. 

The region of visibility of the transit of 1882 will be quite 
different from that of 1874, as it will include the whole Amer- 
ican continent, except some portions in or near the arctic cir- 
cle. The beginning will be visible over a large part of Afri- 
ca, and the end over most of the Pacific Ocean. The most 
favorable northern stations for its observation are in the East- 
ern and Middle States. 

§ 4. Other Methods of determining the Sun's Distance, and their 

Results. 

The methods of determining the astronomical unit which 
we have described rest entirely upon measures of parallax, an 
angle which hardly ever exceeds 20", and which it is there- 
fore exceedingly difficult to measure with the necessary ac- 
curacy. If there were no other way than this of determining 
the sun's distance, we might despair of being sure of it with- 
in 200,000 miles. But the refined investigations of modern 
science have brought to light other methods, by at least two 
of which we may hope, ultimately, to attain a greater degree 
of accuracy than we can by measuring parallaxes. Of these 
two, one depends on the gravitating force of the sun upon the 
moon, and the other upon the velocity of light. 

Parallactic Equation of the Moon. — The motion of the moon 
around the earth is largely affected by the gravitating force 
of the sun, or, to speak more exactly, by the difference of the 
gravitating force of the sun upon the moon and upon the 
earth. A part of this difference depends upon the proportion 
between the respective distances of the moon and the sun, so 
that when this force is known, the proportion can be deter- 



METHODS OF DETERMINING THE SUN'S DISTANCE. 199 

mined. The distance of the moon being known with all nec- 
essary precision, we have only to multiply it by the proportion 
thus obtained to get the distance of the sun. The force in 
question shows itself by producing a certain inequality in the 
moon's motion, by which she falls two minutes behind her 
mean place near the first quarter, and is two minutes ahead 
near her last quarter. In determining this inequality, we have 
to measure an angle about six times as great as the average 
of the planetary parallaxes on which the sun's distance de- 
pends ; so that, if we could measure both angles with the same 
precision, the error, by using the moon, would bo only one- 
sixth as great as in direct measures of parallax. But it seems 
as if nature had determined to allow mankind no royal road 
to a knowledge of the sun's distance. It is the position of 
the moon's centre which we require for the purpose in ques- 
tion, and this can never be directly fixed. We have to make 
our observations on the limb or edge of the moon, as illu- 
minated by the sun, and must reduce our observations to the 
moon's centre, before we can use them. The worst of the 
matter is, that one limb is observed at the first quarter, and 
another at the third quarter, so that we cannot tell with abso- 
lute certainty how much of the observed inequality is real, 
and how much is due to the change from one limb to the other. 
So great is the uncertainty here that, previous to 1854, it was 
supposed that the inequality in question was about 122", 
agreeing with the theoretical inequality from Encke's errone- 
ous value of the solar parallax. Hansen then found that it 
was really about 4" greater, and thus was led to the conclusion 
that the parallax of the sun must be increased, and his distance 
diminished, by one-thirtieth of the whole amount. 

It is quite likely that by adopting improved modes of ob- 
servation, it will be found that the sun's distance can be more 
accurately measured in this way than through the parallaxes 
of the planets. Some pains have already been taken to deter- 
mine the exact amount of the inequality from observations, 
the result being 125 "5. The entire seconds may here be re- 
lied on, but the decimal is quite uncertain. We can only say 



200 PRACTICAL ASTRONOMY. 

that we are pretty surely within three or four tenths of a sec- 
ond of the truth. From this value the parallax of the sun is 
found to be 8".83, with an uncertainty of two or three hun- 
dredths of a second. 

Sun's Distance from the Velocity of Light. — There is an ex- 
traordinary beauty in this method of measuring the sun's dis- 
tance, arising from the contrast between the simplicity of the 
principle and the profoundness of the methods by which alone 
the principle can be applied. Suppose we had a messenger 
whom we could send to and fro between the sun and the 
earth, and who could tell, on his return, exactly how long it 
took him to perform his journey ; suppose, also, we knew the 
exact rate of speed at which he travelled. Then, if we mul- 
tiply his speed by the time it took him to go to the sun, we 
shall at once have the sun's distance, just as we could deter- 
mine the distance of two cities when we knew that a train 
running thirty miles an hour required seven hours to pass be- 
tween them. Such a messenger is light. It has been found 
practicable to determine, experimentally, about how fast light 
travels, and to find from astronomical phenomena how long 
it takes to come from the sun to the earth. How these de- 
terminations are made will be shown in the next chapter; 
here we shall stop only to give results. It is found by Fou- 
cault's experiment that light travels about 185,200 miles per 
second ; and it is known from a study of several astronomical 
phenomena that it passes from the sun to the earth in 498 sec- 
onds. The product of these numbers gives a distance of 
92,230,000 miles, a result, however, which is uncertain by -j-J-^- 
of its entire amount, or nearly half a million of miles, owing to 
the uncertainty in each of the factors. This result was reached 
in 1862, and was one of the first confirmations of the increased 
value of the solar parallax found by Hansen. But since that 
time a redetermination of the velocity of light has been made 
by Cornu, of Paris, by a method soon to be described, with a 
different result. He finds a velocity of 300,400 kilometres or 
186,670 miles per second, making the distance of the sun 
92,960,000 miles, and its parallax 8".794. This discrepancy 



METHODS OF DETERMINING THE SUN'S DISTANCE. 201 

is not yet explained, and the truth can be reached only by a 
repetition of one or both of the experiments. 

These two methods of determining the distance of the sun 
may fairly be regarded as equal in accuracy to that by tran- 
sits of Venus when they are employed in the best manner. 
There are also two or three minor methods which, though 
less accurate, are worthy of mention. One of the most in- 
genious of these was first applied by Leverrier. It is known 
from the theory of gravitation that the earth, in consequence 
of the attraction of the moon, describes a small monthly orbit 
around the common centre of gravity of these two bodies, cor- 
responding to the monthly revolution of the moon around the 
earth, or, to speak with more precision, around the same com- 
mon centre of gravity. If we know the mass (or weight) of 
the moon relatively to that of the earth, and her distance, we 
can thus calculate the radius of the little orbit referred to. 
In round numbers, it is 3000 miles. This monthly oscillation 
of the earth will cause a corresponding oscillation in the lon- 
gitude of the sun, and by measuring its apparent amount we 
can 'tell how far the sun must be placed to make this amount 
correspond to, say 3000 miles. Leverrier found the oscilla- 
tions in arc to be 6".50. From this he concluded the solar 
parallax to be 8".95. But Mr. Stone," of Greenwich, found 
two errors in Leverrier's computation, + and, when these are 
corrected, the result is reduced to S".S5. 

Another recondite method has been employed by Leverrier. 
It is founded on the principle that when the relative masses 
of the sun and earth are known, their distance can be found 
by comparing the distance which a heavy body will fall in 
one second at the surface of the earth with the fall of the lat- 
ter towards the sun in the same time. The mass of the earth 
was found by its disturbing action on the planets Venus and 
Mars, as explained in the chapter on Gravitation. Leverrier 

* Mr. E. J. Stone was then first assistant at the Royal Observatory. Green- 
wich, but has been Astronomer Royal at the Cape of Good Hope since 1^70. 

+ "Monthly Notices of the Royal Astronomical Society,'' vol. xxvii., p. 241, 
and vol. xxviii., pp. 22, 23. 



202 PRACTICAL ASTRONOMY. 

concluded that this method gave the value of the solar paral- 
lax as 8". 86. But one of his numbers requires a small correc- 
tion, which reduces it to 8 ;/ .83. Another determination of the 
mass of the earth relative to that of the sun has recently been 
made by Von Asten, of Pulkowa, from the action of the earth 
upon Encke's comet. The solar parallax thence resulting is 
9".009, the largest recent value ; but the anomalies in the ap- 
parent motions of this comet are such that very little reliance 
can be placed upon this result 

Yet another method of determining the solar parallax has 
been proposed and partially carried out by Dr. Galle.* It 
consists in measuring the parallax of some of the small plan- 
ets between Mars and Jupiter at the times of their nearest 
approach to the earth, by observations in the northern and 
southern hemispheres. The least distance of the nearest of 
these bodies from us is little less than that of the sun, so that 
in this respect they are far less favorable than Venus and 
Mars. But they have the great advantage of being seen in 
the telescope only as points of light, like stars, and, in conse- 
quence, of having their position relative to the surrounding 
stars determined with greater precision than can be obtained 
in the case of disks like those of Venus and Mars. Observa- 
tions of Flora were made in this way at a number of observa- 
tories in both hemispheres during the opposition of 1874, from 
which Dr. Galle has deduced 8".875 as the value of the solar 
parallax. 

Most Probable Value of the Surfs Parallax. — It will be 
seen that the various methods which we have described, ex- 
cepting one or two which are extremely uncertain, give values 
of the solar parallax ranging from 8 ".76 to 8". 88, the most 
reliable determinations being nearer the smaller value. Tak- 
ing them all into consideration, it seems probable that the 
parallax lies either between or very near the limits 8".79 and 
8".83. The corresponding limits of distance are 92,570,000 

* Dr. J. G. Galle, now director of the observatory at Breslau, Eastern Prussia. 
He was formerly assistant at the Observatory of Berlin, where he became cele- 
brated as the optical discoverer of the planet Neptune. 



STELLAR PARALLAX. 203 

and 93,000,000 of miles. It is therefore probable that the true 
distance is 92,000,000, and some fraction, greater than one-half, 
of another million. After all the observations of the recent 
transit of Venus are combined and investigated, we may hope 
to find the uncertainty brought between yet narrower limits. 

In many recent works the distance in question will be found 
stated at 91,000,000 and some fraction. This arises from the 
circumstance that into several of the first determinations by 
the new methods small errors and imperfections crept, which, 
by a singular coincidence, all tended to make the parallax too 
great, and therefore the distance too small. For instance, 
Hansen's original computations from the motion of the moon 
led him to a parallax of 8".96. Revising his calculations, he 
reduced it to 8".917. When his lunar tables, published in 
1857, came to be compared with observations, it was found 
that his parallactic inequality was undoubtedly too great by 
one second or more. When this is corrected, the parallax is 
reduced about a tenth of a second more. 

The observations of Mars, in 1862, as reduced by Winnecke 
and Stone, first led to a parallax of 8".92 to S".94. But in 
these investigations only a small portion of the observations 
was used. When the great mass remaining was joined with 
them, the result was 8 ".85. 

The early determinations of the time required for light to 
come from the sun were founded on the extremely uncertain 
observations of eclipses of Jupiter's satellites, and were five to 
six seconds too small. The time, 493 seconds, being used in 
some computations instead of 498 seconds, the distance of the 
sun from the velocity of light was made too small. 

In both of Leverrier's methods some small errors of computa- 
tion have been found, the effect of all of which is to make his 
parallax too great. Correcting these, and making no change in 
any of his data, the results are respectively S".S5 and 8".83. 

§ 5. Stellar Parallax. 

It is probable that no one thing tended more strongly to 
impress the minds of thoughtful men in former times with 



204: PRACTICAL ASTRONOMY. 

the belief that the earth was immovable than did the absence 
of stellar parallax. We may call to mind that the annual par- 
allax of the fixed stars arises from the change in their direc- 
tion produced by the motion of the earth from one side of 
its orbit to the other. One of the earliest forms in which we 
may suppose this parallax to have been looked for is shown 
in Fig. 58. Suppose AB to be the earth's orbit with the sun, 

R a • T 




Fig. 58.— Effect of stellar parallax. 

S, near its centre, and RT two stars so situated as to be direct- 
ly opposite each other when the earth is at A ; that is, when 
the direction of each star is 90° distant from that of the sun. 
Then it is clear that, after six months, when the earth is at B, 
the stars will no longer be opposite each other, the point U, 
which is opposite B, making the angle TBU, with the direc- 
tion of T. The stars will all be displaced in the same direc- 
tion that the sun is in from the earth. When it was found 
that the most careful observations showed no such displace- 
ment, the conclusion that the earth did not move seemed in- 
evitable. We have seen how Tycho was led in this way to 
reject the doctrine of the earth's motion, and favor a system 
in which the sun moved around it. In this Tycho was fol- 
lowed by the ecclesiastical astronomers who lived during the 
seventeenth century, and who, finding no parallax whatever to 
any of the stars, were led to reject the Copernican system. 

The telescope furnishing so powerful an auxiliary in meas- 
uring small angles, it was natural that the defenders of the 
Copernican system should be anxious to employ it in detect- 
ing the annual parallax of the stars. But the earlier observ- 
ers had very imperfect notions of the mechanical appliances 
necessary to do this with success, and, in consequence, the in- 
vention of the telescope did not result in any immediate im- 



STELLAR PARALLAX. 205 

provement in the methods of celestial measurement. A step 
was taken in 1669 by Hooke, of England, who was among the 
first to see how the telescope was to be applied in the meas- 
urement of the apparent distances of the stars from the ze- 
nith. He fixed a telescope thirty-six feet long in his house, in 
a vertical position, the object-glass being in an opening in the 
roof, while the eye-piece was in one of the lower rooms. A 
fine plumb-line hung down from the object-glass to a point 
below the eye -piece, which gave a truly vertical line from 
which to measure. The star selected for observation was y 
Draconis, because it was comparatively bright, and passed over 
the zenith of London. His mode of observation was to meas- 
ure the distance of the image of the star from the plumb-line 
from day to day at the moment of its passing the meridian. 
He had made but four observations when his object-glass was 
accidentally broken, and the attempt ended without leading 
to any result whatever. 

Between 1701 and 1704, Roemer, then of Copenhagen, at- 
tempted to determine the sum of the double parallaxes of 
Sirius and a Lyrre by the principle shown in Fig. 5S. These 
stars lie somewhere near the opposite quarters of the celestial 
sphere, and the angle between them will vary from spring to 
autumn by nearly double the sum of their parallaxes. The 
angle was measured by the transit instrument and the astro- 
nomical clock, by noting the time which elapsed between the 
transit of Sirius over the meridian, and that of a Lyra?. This 
time was found to be, on the average, 

Hre. Min. Sec. 

In February, March, and April 11 54 59.7 

In September and October 11 54 55.4 

Difference 4. 3 

Here was a difference of four seconds of time, or a minute of 
angle, which was then very naturally attributed to the motion 
of the earth, and which was afterwards printed in a disserta- 
tion entitled " Copernicus Triumphans." It is now known that 
there is no such parallax as this to either of these stars, and 



206 PRACTICAL ASTRONOMY. 

Peters* has shown that the difference which was attributed 
to parallax by the enthusiastic Danish astronomers really arose, 
in great part, from the diurnal irregularity in the rate of their 
clock, caused by the action of the diurnal change of tempera- 
ture upon the uncompensated pendulums. In the spring the 
interval of time measured elapsed during the night, Sirius 
passing the meridian in the evening, and a Lyrse in the morn- 
ing. The cold of night made the clocks go too fast, and so 
the measured interval came out too great. In the autumn 
Sirius passed in the morning, and a Lyrse in the evening ; the 
clock was going too slow on account of the heat of the day, 
and the interval came out too small. 

Among the numerous other vain efforts made by the astron- 
omers of the last century to detect the stellar parallax, that of 
Bradley is worthy of note, owing to the remarkable discovery 
of the aberration of light to which it led. The principle of 
his instrument was the same as that of Hooke, the zenith dis- 
tance of the star y Draconis at the moment of its passing the 
meridian being determined by the inclination of a telescope to 
a fine plumb-line. The instrument thus used, which has be- 
come so celebrated in the history of astronomy, has since been 
known as Bradley's zenith sector. In accuracy it was a long- 
step in advance of any which preceded it, so that by its means 
Bradley was able to announce with certainty that the star in 
question had no parallax approaching a single second. But 
he found another annual oscillation of a very remarkable 
character, arising from the progressive motion of light, which 
will be described in the next chapter. It has frequently hap- 
pened in the history of science that an investigation of some 
cause has led to discoveries in a different direction of an en- 
tirely unexpected character. 

It would be tedious to describe in detail all the efforts 
made by astronomers, during the last century and the early 
part of the present one, to detect the stellar parallax. It will 



* C. A. F. Peters, then of the Pulkowa Observatory, and now editor of the As- 
tronomische Nachrichten. 



STELLAR PARALLAX. 207 

be sufficient to say, in a general way, that they depended on 
absolute measures ; that is, the astronomer endeavored, gen- 
erally by a divided circle, to determine from day to day the 
zenith distance at which the star passed the meridian. The 
position of the zenith was determined in various ways — some- 
times by a fine plumb-line, sometimes by the level of quick- 
silver. What is required is the angle between the plumb-line 
and the line of sight from the observer to the star. The same 
result can be obtained by observing the angle between a ray 
coming directly from a star and the ray which, coming from 
the star, strikes the surface of a basin of quicksilver, and is re- 
flected upwards. Whatever method is used, a large angle has 
to be measured, an operation which is always affected by un- 
certainty, owing to the influences of varying temperatures and 
many other causes upon the instrument. The general result 
of all the efforts made in this way was that while several of 
the brighter stars seemed to some astronomers to have paral- 
laxes, sometimes amounting to two or three seconds, though 
generally not much exceeding a second, yet there was no sueh 
agreement between the various results as was necessary to in- 
spire confidence. As a matter of fact, we now know that 
these results were entirely illusory, being due, not to parallax, 
but to the unavoidable errors of the instruments used. 

Struve was the first one to prove conclusively that the par- 
allaxes even of the brighter stars were so small as to abso- 
lutely elude every mode of measurement before adopted. In 
principle his method was that employed by Roemer, the sum 
of the parallaxes of stars twelve hours distant in right ascen- 
sion being determined by the annual change in the intervals 
between their times of transit over the meridian. But he 
made the great improvement of selecting stars which could 
be observed as they passed the meridian below the pole, as 
well as above it, so that a short time before or after observing 
the transit of a star he could turn his transit instrument be- 
low the pole, and observe the transit of the opposite star from 
west to east. Thus he was not under the necessity of depend- 
ing on the rate of his clock for more than an hour or two, 

15 



208 PRACTICAL ASTRONOMY. 

while Roemer had to depend on it for twelve hours. The re- 
sult of Struve w r as that the average parallax of the twenty- 
live brightest stars within 45° of the pole could not much, if 
at all, exceed a single tenth of a second. 

Such was the general state of things up to the year 1835. 
It was then decided by Struve and Bessel, in lieu of attempt- 
ing to determine zenith distances, to adopt the method of 
relative parallaxes. The idea of this method really dates al- 
most from the invention of the telescope. It was considered 
by Galileo and Huyghens that where a bright and a faint 
star were seen side by side in the field of view of a telescope, 
the latter was probably vastly more distant than the former, 
and that consequently they would change their relative po- 
sition as the earth moved from one side of the sun to the oth- 
er. If, for instance, one star was three times the distance of 
the other, its apparent motion produced by parallax would be 
only a third that of the other, and there would remain a rel- 
ative parallax equal to two-thirds that of the brighter star, 
which could be detected by measuring the angular distance 
of the two stars as seen in the telescope from day to day 
throughout the year. The drawback to which this method is 
subject is the impossibility of determining how many times 
farther the one star is than the other ; in fact, it may be that 
the smaller star is really no farther than the large one. No 
doubt it was this consideration which deterred the astrono- 
mers of the last century from trying this very simple method. 

The astronomers of the last generation found cases in 
which there could be little doubt that a star was much near- 
er to us than the small stars which surrounded it in the field 
of the telescope. For instance, the star 61 Cygni, or rather 
the pair of stars thus designated, are found not to occupy a 
fixed position in the celestial sphere, like the surrounding 
small stars, but to be moving forward in a straight line at the 
rate of six seconds per year. This amount of proper motion 
was so unusual as to make it probable that the star must be 
one of the nearest to us, although it was only of the sixth mag- 
nitude. It was therefore selected by Bessel for the investi- 



STELLAR PARALLAX. 

gation of its parallax relative to two other stars in its neigh- 
borhood. The instrument used was the helionieter, an in- 
strument which, as now made, admits of great precision, but 
which was then liable to small uncertainties from various 
causes. His early attempts to detect a parallax failed aa 
completely as had those of former observers. He recom- 
menced them in August, 1837, his first series of measures be- 
ing continued until October, 1838. The result of this Be 
Tvas the detection of a parallax of about three-tenths of a sec- 
ond (0".3136). He then took down his instrument, made some 
improvements in it, and commenced a second series, which he 
continued until July, 1839 ; and his assistant, Schliiter, until 
March, 1840. The final value of the parallax deduced by 
Bessel from all these observations was 0".35. The reality of 
this parallax has been well established by subsequent investi- 
gators, only it has been found to be a little larger. From a 
combination of all the results, Auwers, of Berlin, finds the 
most probable parallax to be 0".51. 

The star selected by Struve for the measure of relative par- 
allax was the bright one a Lyra*. This has not only a sensible 
proper motion, but is of the first magnitude; so that there is 
every reason to believe it to be among those which are nearest 
to us. The comparison was made with a single very small 
star in the neighborhood, the instrument used being the nine- 
inch telescope of the Dorpat Observatory. The observations 
extended from November, lS35,to August, 1S3S. The result 
was a relative parallax of a quarter of a second. Subsequent 
investigations have reduced this parallax to two-tenths of a 
second, so that although a Lyrae is nearly a hundred times as 
bright as either of the pair of stars 61 Cygni, it is more than 
twice as far from us. 

So far as is known, and, beyond all reasonable doubt, in re- 
ality, the nearest fixed star is a Centauri, in the southern hem- 
isphere. This fact was discovered by Henderson, the English 
Astronomer Royal at the Cape of Good Hope, about the same 
time that Struve and Bessel were making their first measures 
of parallaxes. The observations on which it was founded 



210 PRACTICAL ASTRONOMY. 

were made with the mural circle of the Cape Observatory, 
and were therefore absolute measures of zenith distance, in- 
stead of comparisons with surrounding stars, like the measures 
of Struve and Bessel. From a discussion of his own observa- 
tions, and a very careful series by his successor, Hender- 
son found the parallax of the pair of stars which compose 
a Centauri to be 0".91.* This parallax corresponds to the 
distance of 226,000 astronomical units, f or more than twenty 
millions of millions of miles. Yet it is not only the nearest 
star, but so far the nearest that no other is known to be with- 
in nearly double the distance. 

The most elaborate measures of stellar parallax made in 
recent times are those by Dr. Briinnow, formerly director of 
the observatory at Ann Arbor, Michigan. On his appointment 
to the post of Astronomer Royal for Ireland, Dr. Briinnow 
employed the equatorial telescope of the Dunsink Observa- 
tory in such determinations with great success. The results 
of his measures, with those of other astronomers, are given in 
the Appendix to the present work. 

The recent researches of various observers have resulted in 
showing that there are about a dozen stars visible in our lati- 
tudes of which the parallax ranges from a tenth to half a sec- 
ond. Part of these are small stars, supposed to be near us 
from their large proper motion, while others are stars of the 
far brighter classes. It is, however, remarkable that among the 
thirteen stars of the first magnitude visible in our latitudes, 
less than half have been found to have any measurable paral- 
lax, even when the greatest refinements have been applied in 
the observations. For the most part, the stars with a decided 
parallax are not of a conspicuous magnitude. The two stars 
next in distance to a Centauri are 61 Cygni, of the fifth mag- 
nitude, and one in Ursa Major without a name, and too small 

* The mean of all the measures of the parallax of this pair of stars hitherto 
made, gives 0".93 as their most probable parallax, corresponding to a distance 
of 221,000 astronomical units. 

t The astronomical unit is the distance of the earth from the sun, about 92|- 
millions of miles. 



STELLAR PARALLAX. 211 

to be seen without a telescope. The parallax of the latter has 
been found by Professor Winnecke* to be 0".501, which is 
nearly the same as that of 61 Cygni. The question of the 
average distance of the stars of the first magnitude must 
therefore be regarded as still unsolved. We can only say 
that the parallax of at least half of them is probably less than 
the tenth of a second, and, therefore, the distance greater than 
two million radii of the earth's orbit. f 

In these measurements of the annual parallax of the fixed 
stars, it sometimes happens that the astronomer finds his ob- 
servations to give a negative parallax. To understand what 
this means, we remark that a determination of the distance of 
a star is made by determining its directions, as seen from op- 
posite points of the earth's orbit. If we draw a line from 
each of these points, in the observed direction of the star, the 
point in which the lines meet marks the position of the star. 
A negative parallax shows that the two lines, instead of con- 
verging to a point, actually diverge, so that there is no pos- 
sible position of the star to correspond to the observations. 
Such a paradoxical result can arise only from errors of obser- 
vation. 



* Dr. A. Winnecke, formerly assistant at the Pulkowa Observatory, and now 
director of the observatory at Strasbarg. 

t A list of the stars of which the parallaxes have been determined will be found 
in the Appendix. 



212 PRACTICAL ASTRONOMY. 



CHAPTEE IV. 

THE MOTION OF LIGHT. 

Intimately connected with celestial measurements are the 
curious phenomena growing out of the progressive move- 
ment of light. It is now known that when we look at a star 
we do not see the star that now is, but the star that was sev- 
eral years ago. Though the star should suddenly be blotted 
out of existence, we should still see it shining for a number 
of years before it would vanish from our sight. We should 
see an event that was long past, perhaps one that was past 
before we were born. This non-coincidence of the time of 
perception with that of occurrence is owing to the fact that 
light requires time to travel. We can see an object only by 
light which emanates from it and reaches our eye, and thus 
our sight is behind time by the interval required for the light 
to travel over the space which separates us from the object. 

It was by observations of the satellites of Jupiter that it 
was first found that celestial phenomena were thus seen be- 
hind time. These bodies revolve round Jupiter much more 
rapidly than our moon does around the earth, the inner satel- 
lite making a complete revolution in eighteen hours. Owing 
to the great magnitude of Jupiter and his shadow, this satel- 
lite, as also the two next outside of it, are eclipsed at every rev- 
olution. The accuracy with which the times of disappearance 
in the shadow could be observed, and the consequent value of 
such observations for the determination of longitudes, led the 
astronomers of the seventeenth century to make tables of the 
times of occurrence of these eclipses. In attempting to im- 
prove the tables of his predecessors, it was found by Roemer 
(then of Paris, though a Dane by birth) that the times of the 



THE MOTION OF LIGHT. 213 

eclipses could not be represented by an equable motion of 
the satellites. He could easily represent the times of the 
eclipses when Jupiter was in opposition to the sun, and there- 
fore the earth nearest to Jupiter. But then, as the eartli re- 
ceded from Jupiter in its annual course round the sun, the 
eclipses were constantly seen later, until, when it was at its 
greatest distance from Jupiter, the times appeared to be '"I'l 
minutes late. Such an inequality, Roemer concluded, could 
not be real; he therefore attributed it to the fact that it must 
take time for light to come from Jupiter to the eartli, and 
that this time is greater the more distant the earth is from 
the planet. He therefore concluded that it took light 22 
minutes to cross the orbit of the earth, and, consequently, 11 
minutes to come from the sun to the earth. 

The next great step in the theory of the progressive motion 
of light was made by the celebrated Bradley, afterwards As- 
tronomer Royal of England, to whose observations at Kew on 
the star y Draconis with his zenith sector, in order to deter- 
mine the parallax of the star, allusion has already been made. 
The effect of parallax would have been to make the declina- 
tion greatest in June and least in December; while in March 
and September the star would occupy an intermediate or 
mean position. But the actual result of the measures was 
entirely different, and exhibited phenomena which Bradley 
could not at first account for. The declinations of June and 
December were the same, showing no effect of parallax. But, 
instead of remaining the same the rest of the year, the decli- 
nation was some forty seconds greater in September than in 
March, when the effect of parallax should be the same. Thus, 
the star had a regular annual oscillation ; but instead of its 
apparent motion in this little orbit being opposite to that of 
the earth in its annual orbit, as required by the laws of rela- 
tive motion, it was constantly at right angles to it. 

After long consideration, Bradley saw the cause of the 
phenomenon in the progressive motion of light combined 
with the motion of the earth in its orbit. In Fig. 59 let S 
be a star, and OT a telescope pointed at it. Then, if the 



214: PRACTICAL ASTRONOMY. 

telescope is not in motion, the ray SOT emanating from the 
star, and entering the centre of the object-glass, 
will pass down near the right-hand edge of the eye- 
piece, and the star will appear in the right of the 
field of view. But, instead of being at rest, all onr 
telescopes are carried along with the earth in its 
orbit round the sun at the rate of nearly nineteen 
miles a second. Suppose this motion to be in the 
direction of the arrow; then, while the ray is pass- 
ing down the telescope, the latter moves a short dis- 
tance, so that the ray no longer strikes the right- 
hand edge of the eye-piece, but some point farther 
to the left, as if the star were in the direction S' 9 
and the ray followed the course of the dotted line. 
In order to see the star centrally, the eye end of the 
QT telescope must be dropped a little behind, so that, 
fig. 59. — instead of pointing in the direction S, it will really 
Aberration b e pointing in the direction S', shown by the dotted 
ray. This will then represent the apparent direc- 
tion of the star, which will seem displaced in the direction in 
which the earth is moving. 

The phenomenon is quite similar to that presented by the 
apparent direction of the wind on board a steamship in mo- 
tion. If the wind is really at right angles to the course of the 

■zoo 

ship, it will appear more nearly ahead to those on board ; and 
if two ships are passing each other, they will appear to have 
the wind in different directions. Indeed, it is said to have 
been through noticing this very result of motion on board a 
boat on the Thames, that the cause of the phenomenon he 
had observed was suggested to Bradley. 

The displacement of the stars which we have explained is 
called the Aberration of Light Its amount depends on the ra- 
tio of the velocity of the earth in its orbit to the velocity of 
light. It can be determined by observing the declination of 
a star at the proper seasons during a number of years, by 
which the annual displacement will be shown. The value 
now most generally received is that determined by Struve at 



THE MOTION OF LIGHT 215 

the Pulkowa Observatory, and is 20".445. Though this is the 
most reliable value yet found, the two last figures are both 
uncertain. We can say little more than that the constant 
probably lies between 20".43 and 20".48, and that, if outside 
these limits at all, it is certainly very little outside. 

This amount of aberration of each star shows that light 
travels 10,089 times as fast as the earth in its orbit. From 
this we can determine the time light takes to travel from the 
sun to the earth entirely independent of the satellites of Ju- 
piter. The earth makes the circuit of its orbit in 365 J days. 
Then light would make this same circuit in ]i^ | of a day. 
which we find to be 52 minutes 8-| seconds. The diameter 
of the earth's orbit is found by dividing its circumference by 
3.1416, and the mean distance of the sun is half this diameter. 
We thus find from the above amount of aberration that light 
passes from the sun to the earth in 8 minutes 18 seconds. 

The question now arises, Does the same result follow from 
the observations of the satellites of Jupiter? If it does, we 
have a striking confirmation of the astronomical theory of the 
propagation of light. If it does not, we have a discrepancy, 
the cause of which must be investigated. We have said that 
the first investigator of the subject found the time required 
to be 11 minutes. This determination was, however, uncertain 
by several minutes, owing to the very imperfect character 
of the early observations on which Roemer had to depend. 
Early in the present century, Delambre made a complete in- 
vestigation from all the eclipses of the satellites which had 
been observed between 1662 and 1802, more than a thousand 
in number. His result was 8 minutes 13.2 seconds. 

There is a discrepancy of five seconds between this result 
of Delambre, obtained some seventy years ago, and the mod- 
ern determinations of the aberrations of the fixed stars made 
by Struve and others. What is its cause ? Probably only the 
errors of the observations used by Delambre. In this case, 
there would be no real difference. But some physicists and 
astronomers have endeavored to show that there is a real 
cause for such a difference, which they hold to indicate an er- 



216 PRACTICAL ASTRONOMY. 

ror in the value of the aberration derived from observation 
arising in this way. It is known from experiment that light 
passes through glass or any other refracting medium more 
slowly than through a void. In observations with a telescope 
the light has to pass through the objective, and the time lost 
in doing so will make the aberration appear larger than it 
really is, and the velocity of light will appear too small. But 
the commonly received theory (that of Fresnel) is that this 
loss of time is compensated by the objective partially drawing 
the ray with it. Desirous of setting the question at rest, Pro- 
fessor Airy, a few years ago, constructed a telescope, which 
he filled with water, with which he observed the constant of 
aberration. The aberration was found to be the same as with 
ordinary telescopes, thus proving the theory of Fresnel to be 
correct, because on the other theory the aberration ought to 
have been much increased by the water. 

Hence this explanation of the difference of the two results 
fails, and renders it more probable that there is some error in 
Delambre's result. A reinvestigation of all the observations 
of Jupiter's satellites is very desirable ; but so vast is the labor 
that no one since Delambre has undertaken it. Mr. Glasenapp, 
a young Russian astronomer, has, however, recently investi- 
gated all the observations of Jupiter's first satellite made dur- 
ing the years 1848-1873, and found from these that the time 
required for light to pass from the sun to the earth is 8 min- 
utes 20 seconds. Instead of being smaller than Struve's re- 
sult, this is two seconds larger, and seven seconds larger than 
that of Delambre. It is therefore concluded that the differ- 
ence between the results of the two methods arises entirely 
from the errors of the observations used by Delambre, and 
that Struve's time (498 seconds) is not a second in error. 

Each of the two methods we have described gives us the 
time required for light to pass from the sun to the earth ; but 
neither of them gives us any direct information respecting the 
velocity of light. Before we can determine the latter from 
the former, we must know what the distance of the sun is. 
Dividing this distance in miles by 498, we shall have the dis- 



THE MOTION OF LIGHT. 217 

tance which light travels in a second. Conversely, if we can 
find experimentally how far light travels in a second, then by 
multiplying this distance by 498 we shall have the distance of 
the sun. But we need only reflect that the velocity of light 
is about 180,000 miles per second to see that the problem of 
determining it experimentally is a most difficult one. It is 
seldom that objects on the surface of the earth are distinctly 
seen at a greater distance than forty or fifty miles, and over 
such a distance light travels in the forty-thousandth part of a 
second. As might be expected, the earlier attempts to fix the 
time occupied by light in passing over distances so short as 
those on the surface of the earth were entire failures. The 
first of these is due to Galileo; and his method is worth men- 
tioning, to show the principle on which such a determination 
can be made. He stationed two observers a mile or two apart 
by night, each having a lantern which he could cover in a 
moment. The one observer, A, was to cover his lantern, and 
the distant one, B, as soon as he saw the light disappear, cov- 
ered his also. In order that A might see the disappearance 
of B's lantern, it was necessary that the light should travel 
from A to B, and back again. For instance, if it took one 
second to travel between the two stations, B would continue 
to see A's light an entire second after it was really extinguish- 
ed ; and if he then covered his lantern instantly, A would 
still see it during another second, making two seconds in all 
after he had extinguished his own, besides the time B might 
have required to completely perform the movement of cover- 
ing his. 

Of course, by this rough method Galileo found no inter- 
val whatever. An occurrence which only required the hun- 
dredth part of the thousandth of a second was necessarily in- 
stantaneous. But we can readily elaborate his idea into the 
more refined methods used in recent times. Its essential feat- 
ure is that which must always be employed in making the de- 
termination ; that is, it is necessary that the light shall be sent 
from one station to another, and then returned to the first 
one, where the double interval is timed. There is no possi- 



218 



PRACTICAL ASTRONOMY. 



bility of comparing the times at two distant stations with the 
necessary precision. The first improvement we should make 
on Galileo's method would be to set up a mirror at the dis- 
tant station, and dispense with the second lantern, the ob- 
server A seeing his own lantern by reflection in the mirror. 
Then, if he screened his lantern, he would continue to see it 
by reflection in the mirror during the time the light required 
to go and come. But this also would be a total failure, be- 
cause the reflection would seem to vanish instantly. Our next 
effort would be to try if we could not send out a flash of 
light from our lantern, and screen it off before it got back 
again. An attempt to screen off a single flash would also be 
a failure. We should then try sending a rapid succession of 
flashes through openings in a moving screen, and see wheth- 
er they could' be cut off by the sides of the openings before 

their return. This would be 
effected by the contrivance 
shown in Fig. 60. We have 
here a wheel with spokes ex- 
tending from its circumfer- 
ence, the distance between 
them being equal to their 
breadth. This wheel is placed 
in front of the lantern, L, so 
that the light from the latter 

Fig. 60.— Revolving wheel, for measuring the has to paSS between the Spokes 
velocity of light. of ^ wheel {n order t() reach 

the distant mirror. In the figure the reader is supposed to be 
between the wheel and the reflecting mirror, facing the for- 
mer, so that he sees the light of the lantern, and also the eye 
of the observer, between the spokes. The latter, looking be- 
tween the spokes, will see the light of the lantern reflected 
from the mirror. Now, suppose he turns the wheel, still keep- 
ing his eye at the same point. Then, each spoke cutting off the 
light of the lantern as it passes, there will be a succession of 
flashes of light which will pass through between the spokes, 
travel to the mirror, and thence be reflected back again to the 







THE MOTION OF LIGHT. 219 

wheel. Will they reach the eye of the observer behind the 
wheel ? Evidently they will, if they return so quickly that a 
tooth has not had time to intervene. But suppose the wheel to 
turn so rapidly that a tooth just intervenes as the flash gets 
back to it. Then the observer will see no light in the mirror, 
because each successive flash is caught by the following tooth 
just before it reaches the observer's eye. Suppose, next, that 
he doubles the speed of his wheel. Then, while the flash is 
travelling to the mirror and back, the tooth will have passed 
clear across and out of the way of the flash, so that the latter 
will now reach the observer's eye through the opening next 
following that which it passed through to leave the lantern. 
Thus, the observer will see a succession of flashes so rapid 
that they will seem entirely continuous to the eye. If the 
speed of the wheel be again increased, the return flash will be 
caught on the second tooth, and the observer will see no light, 
while a still further increase of velocity will enable him to 
see the flashes as they return through the second interval be- 
tween the spokes, and so on. 

In principle, this is Fizeau's method of measuring the ve- 
locity of light. In place of spokes, he has exceedingly fine 
teeth in a large wheel. He does not look between the teeth 
with the naked eye, but employs a telescope so arranged that 
the teeth pass exactly through its focus. An arrangement is 
made by which the light passes through the same focus with- 
out reaching the observer's eye except by reflection from the 
distant mirror. The latter is placed in the focus of a second 
telescope, so that it can be easily adjusted to send the rays 
back in the exact direction from which they come. To find 
the time it takes the light to travel, it is necessary to know the 
exact velocity of the wheel which will cut off the return light 
entirely, and thence the number of teeth which pass in a sec- 
ond. Suppose, for instance, that the wheel had a thousand 
teeth, and the reflector was nine miles away, so that the light 
had to travel eighteen miles to get back to the focus of the 
telescope. Then it would be found that with a velocity of 
about five turns of the wheel per second, the light would be 



220 



PRACTICAL ASTRONOMY. 



first cut off. Increasing the velocity, it would reappear, and 
would grow brighter until the velocity reached ten turns per 
second. It would then begin to fade away, and at fifteen 
turns per second would be again occulted, and so on. With 
the latter velocity, fifteen thousand teeth and fifteen thousand 
intervals would pass in a second, while two teeth and one in- 
terval passed during the time the light was performing its 
journey. The latter would, therefore, be performed in the 
ten-thousandth part of a second, showing the actual velocity 
to be 180,000 miles per second. The most recent determina- 
tion made in this way is by M. Cornu, of Paris, who has made 
some improvements in the mode of applying it. His results 
will be described presently. 

Ingenious and beautiful as this method is, I do not think it 
can be so accurate as another employed by Foucault, in which 
it is not a toothed wheel which revolves, but a Wheatstone 
mirror. To explain the details of the apparatus actually used 

would be tedious, 
but the principle on 
which the method 
rests can be seen 
quite readily. Sup- 
pose AB, Fig. 61, to 
represent a flat mir- 
ror, seen edgewise, 
revolving round an 
// axis at X, and C a 

Fig. 61.— Illustrating Foucault's method of measuring the fixed COncave 11111*- 
velocity of light. ^ g0 p ] ace ^ thafc 

the centre of its concavity shall fall on X. Let O be a lumi- 
nous point, from which emanates a single ray of light, OX. 
This ray, meeting the mirror at X, is reflected to the concave 
mirror, O, which it meets at a right angle, and is therefore re- 
flected directly back on the line from which it came, first to 
X, and then through the point O, from which it emanated, so 
that an eye stationed at-will see it returning exactly through 
the point O. No matter how the observer may turn the mir- 



Bf* 



AX 




THE MOTION OF LIGHT. 221 

ror AB, he cannot make the reflected ray deviate from this 
line : he can only make it strike a different point of the mir- 
ror C. If he turns AB so that after the ray is reflected from 
it, it does not strike C at all, then he will see no return ray. 
If the ray is reflected back at all, it will pass through 0. This 
result is founded on the supposition that the mirror AB re- 
mains in the same position during the time the ray occupies 
in passing from X to C and back. But suppose the mirror 
AB to be revolving so rapidly that when the ray gets back 
to X, the mirror has moved to the position of the dotted line 
A f B'. Then it will no longer be reflected back through 0, 
but will be sent in the direction E', the angle EXE' being 
double that through which the mirror has moved during the 
time the ray was on its passage. Knowing the velocity of 
the mirror, and the angle EXE', this time is easily found. 

Evidently the observer cannot see a continuous light at E, 
because a reflection can be sent back only when the revolving 
mirror is in such a position as to send the ray to some point 
of the concave mirror, C. What will really be seen, therefore, 
is a succession of flashes, each flash appearing as the revolving 
mirror is passing through the position AB. But when the 
mirror revolves rapidly, these flashes will seem to the eye to 
form a continuous light, which, however, will be fainter than 
if the mirror were at rest, in the proportion which the arc of 
the concave mirror, C, bears to an entire circle. Beyond the 
enfeeblement of the light, this want of continuity is not pro- 
ductive of any inconvenience. It was thus found by Fou- 
cault that the velocity of light was 185,000 miles per second, a 
result which is probably within a thousand miles of the troth. 

The preceding explanation shows the principle of the meth- 
od, but not the details necessary in applying it. It is not 
practicable to isolate a single ray of light in the manner sup- 
posed in the figure, and therefore, without other apparatus, 
the light from would be spread all over the space around E 
and E '. The desired result is obtained by placing a lens be- 
tween the luminous point and the revolving mirror in such 
a position that all the light falling from upon the lens shall, 



222 PBACTICAL ASTRONOMY. 

after reflection, be brought to a focus upon the surface of the 
concave mirror, C. Then when the mirror AB is made to re- 
volve rapidly, the return rays passing back through the lens 
on their return journey 'are brought to a focus at a point 
along-side 0, and distant from it by an amount which is pro- 
portional to the time the light has required to pass from X to 
C and back again. 

So delicate is this method, that the millionth of a second of 
time can be measured by it as accurately as a carpenter can 
measure the breadth of a board with his rule. Its perfection 
is the result of the combined genius of several men. The first 
idea of employing a revolving mirror in the measurement of 
a very minute interval of time is due to the late Sir Charles 
Wheatstone, who thus measured the duration of the electric 
spark. Then Arago showed that it could be applied to de- 
termine whether the velocity of light was greater in water 
or in air. Fizeau and Foucault improved on Arago's ideas 
by the introduction of the concave mirror, having its centre 
of curvature in the revolving mirror, and then this wonderful 
piece of apparatus was substantially complete. The last de- 
termination of the velocity of light with it was made by Fou- 
cault, and communicated to the French Academy of Sciences 
in 1862, with the statement that the velocity resulting from 
all his experiments was 298,000 kilometres (185,200 miles) 
per second. 

The problem in question was next taken up by Cornu, of 
Paris, whose result has already been alluded to. Notwith- 
standing the supposed advantages of the Foucault -Wheat- 
stone method, M. Cornu preferred that of Fizeau. His first 
results, reached in 1872, accorded quite well with those of 
Foucault just cited, indicating a small but somewhat uncer- 
tain increase. His experiments were repeated in 1874, and 
their results were communicated to the French Academy of 
Sciences in December of that year. In this last series of 
measurements his station was the observatory, and the distant 
mirror was placed on the tower of Montlhery, at a distance of 
about fourteen English miles. The telescope through which 



THE MOTION OF LIGHT. 223 

the flashes of light were sent and received was twenty-nine 
feet long and of fourteen inches aperture. The velocity of 
the toothed wheel could be made to exceed 1600 turns a sec- 
ond, and by the electro-chronograph, on which the revolutions 
were recorded, the time could be determined within the thou- 
sandth of a second. At Montlhery, the telescope, in the focus 
of which the reflecting mirror was placed, was six inches in 
aperture, and was held by a large cast-iron tube set in the 
masonry of the tower. At this distance M. Cornu was able, 
with the highest velocity of his revolving wheel, to make 
twenty of its teeth pass before the flashes of light got back, 
and to catch them, on their return, on the twenty-first tooth. 

All the determinations, however, were not made with the 
wheel going at this rate, but with such different velocities that 
the rays were caught sometimes on one tooth and sometimes 
on another, from the fourth to the twenty -first. The follow- 
ing table shows the velocity of light in kilometres per second 
when the ray was caught on the fourth tooth, on the fifth, and 
so on to the twenty-first : 



Tooth 4 300,130 

" 5 300,530 

" G 300,750 

11 7 300,820 

11 8 299,940 

" 9 300,550 

44 10 300,640 

44 11 300,350 

44 12 300,500 



Tooth 13 300,340 

44 14 300,350 

44 15 300,290 

44 16 300,620 

" 17 300,000 

" 18 300,150 

" 19 299,550 

44 20 

" 21 300,0G0 



M. Cornu hence concludes that the velocity of light in air 
is 300,330, and in a vacuum 300,400 kilometres per second. 
But Helmert, of Aix, has noticed a tendency in M. Cornu's 
numbers, as given above, to diminish as the velocity of the 
wheel is increased, and concludes that the true velocity to be 
derived from the measures is 299,990 kilometres. This re- 
sult, though less than that derived by Cornu himself, is still 
nearly 2000 kilometres greater than that of Foucault. 

16 



224 PRACTICAL ASTRONOMY. 



CHAPTER V. 

THE SPECTROSCOPE. 

In one of Dr. Lardner's popular lectures on astronomy, de- 
livered some thirty years ago, he introduced the subject of 
weighing the planets as one in which he could with difficulty 
expect his statements to be received with credulity. That 
men should measure the distances of the planets was a state- 
ment he expected his hearers to receive with surprise ; but the 
step from measuring to weighing was so long a one, that it 
seemed to the ordinary mind to extend beyond all the bounds 
of possibility. 

Had a hearer told the lecturer that men would also be able 
to determine the chemical constituents of the sun and stars, 
and to tell whether any of them did or did not contain iron, 
hydrogen, and other chemical elements, the lecturer would 
probably have replied that that statement quite exceeded the 
limits of his own credulity ; that, while he himself saw clearly 
how the planets were measured and weighed, he looked upon 
the idea of determining their chemical constitution as a mere 
piece of pleasantry, or the play of an exuberant fancy. And 
yet, this very thing has, to a certain extent, been done by the 
aid of the spectroscope. The chemical constitution of matter 
in the state of gas or vapor can be detected almost as readily 
at the distance of the stars as if we had it in our laboratories. 
The difficulties which stand in the way do not arise from the 
distance, but from the fact that matter in the heavenly bodies 
seems to exist in some state which we have not succeeded in 
exactly reproducing in our laboratories. Like many other 
wonders, spectrum analysis, as it is called, is not at all extraor- 
dinary after we see how it is done. Indeed, the only wonder 



THE SPECTROSCOPE* 225 

now is how the first half of this century could have passed 
without physicists discovering it. The essential features of 
the method are so simple that only a knowledge of the ele- 
ments of natural philosophy is necessary to enable them to be 
understood. We shall, therefore, briefly explain them. 

It is familiarly known that if we pass the rays of the sun 
which enter a room by a small opening through a prism, the 
light is separated into a number of bright colors, which arc- 
spread out on a certain scale, the one end being red and the 
other violet, while a long range of intermediate colors is found 
between them. This shows that common white light is really 
a compound of every color of the spectrum. This compound 
is not like chemical compounds, made up of two or three or 
some limited number of simples, but is composed of an infini- 
ty of different kinds of light, all running into each other bv 
insensible degrees ; the difference, however, being only in col- 
or, or in the capacity of being refracted by the prism through 
which it passes. This arrangement of colors, spread out to our 
sight according to the refrangibility of the light which forms 
them, is called the spectrum. B} T the spectrum of any object 
is meant the combination of colors found in the light which 
emanates from that object. For instance, if we pass the light 
from a candle through a prism, so as to separate it into it- 
component colors, and make the light thus separated fall on 
a screen, the arrangement of colors on the screen would be 
called the spectrum of the candle. If we look at a bright 
star through a prism, the combination of colors which we see 
is called the spectrum of the star, and so with any other object 
we may choose to examine. 

As the experiment of forming a spectrum is commonly 
made, there is a slight mixing-up of light of the different col- 
ors, because light of the same degree of refrangibility will 
fall on different parts of the screen according to the part of 
the prism it passes through. When the separation of the light 
is thus incomplete, the spectrum is said to be impure. In or- 
der to make any successful examination of the light which 
emanates from an object, our spectrum must be pure ; that is, 



226 PRACTICAL ASTRONOMY. 

each point of the spectrum must be formed by light of one 
degree of refrangibility. To effect this in the most perfect 
way, the spectrum is not formed on a screen, but on the retina 
of the observers eye. An instrument by which this is done 
is called a spectroscope. 

The most essential parts of a spectroscope consist of a small 
telescope with a prism in front of the object-glass. The ob- 
server must adjust his telescope so that, removing the prism, 
and looking directly at the object, he shall obtain distinct vis- 
ion of it. Then, putting the prism in its place, and turning 
the telescope to such an angle that the light which comes from 
the object shall, after being refracted by the prism, pass direct- 
ly into the telescope, he looks into the latter. When the prop- 
er adjustments are made, he will see a pure spectrum of the 
object. In order that this experiment may succeed, it is es- 
sential that the object, when viewed directly, shall present the 
appearance of a point, like a star or planet. If it is an object 
which has a measurable surface, like the sun or moon, he will 
see either no spectrum at all or only a very impure one. 

For this reason, a spectroscope which consists of nothing but 
a telescope and prism is not fitted for any purpose but that of 
trial and illustration. To fit it for general use, another ob- 
ject-glass, with a slit in its focus, is added. Fig. 62 shows the 





Fig. 62. — Course of rays through a spectroscope. 

essential parts of a modern spectroscope. At the farther end 
of the second telescope, where the light enters, is a narrow 
slit, which can be opened or closed by means of a screw, and 



THE SPECTROSCOPE. 227 

through which the light from the object is admitted. The 
rays of light following the dotted lines are made parallel by 
passing through the lens, L. They then fall on the prism, P, 
by which they are refracted, and from which they emerge par- 
allel, except that the direction of the rays of different colors 
is different, owing to the greater or less degree of refraction 
produced by the prism. They then pass through the object- 
glass of the telescope, T, by which the rays of each color are 
brought to a focus at a particular point in the field of view, 
the red rays all coming together at the lower point, the violet 
ones at the upper point, and those of each intermediate color 
at their proper place along the line. The observer, looking 
into the telescope, sees the spectrum of whatever object is 
throwing its lijHit through the slit. 

If the object of which the observer wishes to see the spec- 
trum is a flame, he places it immediately in front of the slit; 
and if it is an object of sensible surface, like the sun or moon, 
he points the collimator, C, directly at it, so that the light 
which enters the slit shall fall on the lens, L. But if it is a 
star, he cannot get light enough in this way to see it, and he 
must either remove his collimator entirely, or fasten his spec- 
troscope to the end of a telescope, so that the slit shall be 
exactly in the focus. The latter is the method universally 
adopted in examining the spectrum of a star. 

If, with this instrument, we examine the light which comes 
from a candle, from the tire, or from a piece of white-hot 
iron, we shall find it to be continuous; that is, there is no gap 
in the series of colors from one end to the other. But if we 
take the light from the sun, or from the moon, a planet, or 
any object illuminated by the sun, we shall find the spectrum 
to be crossed by a great number of fine dark lines, showing 
that certain kinds of light are wanting. It is now known 
that the particular kinds of light which originally belonged 
in these dark lines have been culled out by the gases surround- 
ing the sun through which the light has passed. This culling- 
out is called Selective Absorption. It is found by experiment 
that each kind of gas has its own liking for light of peculiar 



228 PRACTICAL ASTRONOMY. 

degrees of refrangibility, and absorbs the light which belongs 
in the corresponding parts of the spectrum, letting all the 
other light pass. 

Perhaps we may illustrate this process by a similar one 
which we might imagine mankind to perform. Suppose Nat- 
ure should loan us an immense collection of many millions 
of gold pieces, out of which w T e were to select those which 
would serve us for money, and return her the remainder. 
The English rummage through the pile, and pick out all the 
pieces which are of the proper weight for sovereigns and half- 
sovereigns ; the French pick out those which will make five, 
ten, twenty, or fifty franc pieces ; the Americans the one, five, 
ten, and twenty dollar pieces, and so on. After all the suit- 
able pieces are thus selected, let the remaining mass be spread 
out on the ground according to the respective weights of the 
pieces, the smallest pieces being placed in a row, the next in 
weight in an adjoining row, and so on. We shall then find a 
number of rows missing: one which the French have taken 
out for five-franc pieces; close to it another which the Amer- 
icans have taken for dollars; afterwards a row which have 
gone for half-sovereigns, and so on. By thus arranging the 
pieces, one would be able to tell what nations had culled over 
the pile, if he only knew of what weight each one made its 
coins. The gaps in the places where the sovereigns and- half- 
sovereigns belonged would indicate the English, that in the 
dollars and eagles the Americans, and so on. If, now, we re- 
flect how utterly hopeless it would appear, from the mere ex- 
amination of the miscellaneous pile of pieces which had been 
left, to ascertain what people had been selecting coins from it, 
and how easy the problem would appear when once some 
genius should make the proposed arrangement of the pieces 
in rows, we shall see in what the fundamental idea of spec- 
trum analysis consists. The formation of the spectrum is the 
separation and arrangement of the light which comes from an 
object on the same system by which we have supposed the 
gold pieces to be arranged. The gaps we see in the spectrum 
tell the tale of the atmosphere through which the light has 



THE SPECTROSCOPE. 229 

passed, as in the case of the coins they would tell what nations 
had sorted over the pile. 

That the dark lines in the solar spectrum are picked out by 
the gases of the sun's atmosphere has long been surmised ; in- 
deed, Sir John Ilerschel seems to have had a clear idea of 
the possibility of spectrum analysis half a century ago. The 
difficulty was to find what particular lines any particular sub- 
stance selects; since, to exert any selective action, a vastly 
greater thickness of gas is generally required than it is prac- 
ticable to obtain experimentally. This difficulty was sur- 
mounted by the capital discovery of Kirchhoff and Bunsen, 
that a glowing gas gives out rays of the same decree of refrangHbil- 
ity which it absorbs when light passes through it. For example, 
if we put some salt into the flame of a spirit-lamp, and ex- 
amine the spectrum of the light, we shall find a pair of bright- 
yellow lines, which correspond most accurately to a pair of 
black lines in the solar spectrum. These lines are known to 
be due to sodium, a component of common salt, and their ex- 
istence in the solar spectrum shows that there is sodium 
in the sun's atmosphere. They are therefore called the sodi- 
um lines. By vaporizing various substances in sufficiently hot 
flames, the spectra of a great number of metals and gases 
have been found. Sometimes there are only one or two bright 
lines, while with iron the number is counted by hundreds. 
The quantity of a substance necessary to form these bright 
lines is so minute that the presence of some metals in a com- 
pound have been detected with the spectroscope when it was 
impossible to find a trace of them in any other way. Indeed, 
two or three new metals, the existence of which was before en- 
tirely unknown, first told their story through the spectroscope. 

The general relations of the spectrum to the state of the 
substance from which the light emanated may be condensed 
into three rules, or laws, as follows : 

1. The light from a glowing solid or liquid forms a contin- 
uous spectrum, in which neither bright nor dark lines are 
found. The spectrum is of the same nature, no matter how 
finely the substance may be divided. 



230 PRACTICAL ASTRONOMY. 

2. If the light from the glowing solid passes through a gas- 
eous atmosphere, the spectrum will be crossed by dark lines 
occupying those parts of the spectrum where the light culled 
out by the atmosphere belongs. 

3. A glowing gas sends out light of the same degrees of 
refrangibility as belong to that which it absorbs, so that its 
spectrum consists of a system of bright lines occupying the 
same position as the dark lines it would produce by absorption. 

If, then, on examining the spectrum of a star or other heav- 
enly body, we find only bright lines with dark spaces between 
them, we may conclude that the body consists of a glowing 
gas, and we judge what the gas is by comparing the spectrum 
with those of various substances on the earth. If, on the oth- 
er hand, the spectrum is a continuous one, except where cross- 
ed by fine dark lines, we conclude that it emanates from a 
glowing body surrounded by an atmosphere which culls out 
some of the rays of light. 

It will be seen that the spectroscope gives us no definite in- 
formation respecting the nature or composition of bodies in 
the solid state. If we heat any sort of metal white-hot, sup- 
posing only that it will stand this heat without being vapor- 
ized, we shall have a spectrum continuous from end to end, in 
which there will be neither bright nor dark lines to give any 
indications respecting the substance. In order, therefore, to 
detect the presence of any chemical element with this instru- 
ment, that element must be in the form of gas or vapor. Here 
we have one limitation to the application of the spectroscope 
to the celestial bodies. The tendency of bodies in space is to 
cool off, and when they have once become so cool as to solidi- 
fy, the instrument in question can give us no further definite 
information respecting their constitution. 

Even if the body be in the gaseous state, we cannot always 
rely on the spectroscope informing us with certainty of the 
nature of the gas. The light we analyze must either be emit- 
ted by the gas, the latter being so hot as to shine by its own 
light, or it must be transmitted through it. Thus, the appli- 
cation of spectrum analysis is confined to glowing gases and 



THE SPECTROSCOPE. 231 

the atmospheres of the stars and planets, the application to the 
latter depending on the fact that the sunlight reflected from 
the surface of the planet passes twice through its atmosphere. 
Even in these cases the interpretation of its results is sometimes 
rendered difficult in consequence of the varied spectrum of the 
same gas at different temperatures and under different degrees 
of pressure. Under some conditions so many new lines are 
introduced into the spectrum of hydrogen that it can hardly 
be recognized. As a general rule, the greater the pressure, the 
greater the number of lines which appear; indeed, it has been 
found by Lockyer and Frankland that as the pressure and den- 
sity of a gas are increased, its spectrum tends to become con- 
tinuous. We must therefore regard the third of the above 
rules respecting spectrum analysis, or, rather, the general rule 
that a glowing gas gives a spectrum of bright lines, as not uni- 
versally true. If we could, by artificially varying the temper- 
ature, pressure, and composition of gases, accurately reproduce 
the spectrum of a celestial body, the changes of the spectrum 
which we have mentioned would be a positive advantage ; 
since they would enable us to determine, not merely the com- 
position of a gaseous body, but its temperature and pressure. 
This is, however, a field in which success has not yet been 
reached. 

There is still another circumstance which renders the spec- 
tra of the heavenly bodies more complex than was at first sup- 
posed, but which may, by this very complexity, enable us to 
make great advances in our knowledge of the physical consti- 
tution of the sun and stars. It is that the two classes of spec- 
tra just described — namely, (1) a continuous spectrum crossed 
by dark lines, and (2) a spectrum composed wholly of bright 
lines — are only two extreme cases, and that in many cases 
they are combined in very different proportions. If a white- 
hot body is composed of a glowing atmosphere, the hotter 
substances of this atmosphere may show bright lines, while 
the cooler substances may absorb dark lines from the light 
emitted by the hot body below. Thus, we may have bright 
lines, dark lines, and strips of continuous spectrum all mixed 



232 PRACTICAL ASTRONOMY. 

up in such a way that it may be hard to interpret what is 
seen. The difficulty is to know whether a narrow, dark space 
is produced by the absorption of a gas, or whether it is simply 
an interval between two bright gaseous lines ; and whether a 
narrow, bright space is produced by a glowing gas, or whether 
it is a small strip of continuous spectrum from a glowing solid 
between two absorption bands. We have a mixed-up spec- 
trum of this kind in the Bessemer furnace. The difficulty is 
increased by the fact that the dark portions culled out by the 
absorption of the cooler gases are not always fine perfectly 
dark lines, but in many cases are broad, grayish bands. It is, 
indeed, possible that these bands may be made up of groups 
of fine lines, too close to be separately seen; but so long as the 
separate lines cannot be distinguished, this question must be 
undecided. 

Until very lately, it was always supposed that the spectrum 
of the light of the sun, so far as it could be analyzed, was 
continuous from end to end, except where dark absorption 
lines crossed it. A remarkable addition to this theory has, 
however, been made by Professor Henry Draper, of New 
York, the main point of the addition being that the spectrum 
is crossed by the bright lines and bands arising from glowing 
gases, and that these lines admit of being recognized in cer- 
tain parts of the spectrum if the proper steps are taken to 
bring them out. That bright lines might well exist in the 
spectrum no one would deny, because the gases of the chro- 
mosphere must produce them. But it has always been sup- 
posed that they must be so excessively faint as to be entirely 
invisible when projected on the spectrum of the sun itself, and 
so no one is known to have sought for them with especial 
care. Dr. Draper's course has been to photograph side by 
side the solar spectrum between the lines G and H, and the 
corresponding part of the spectrum of oxygen rendered lumi- 
nous by the electric spark. The result is that out of thirteen 
bright lines of oxygen, some of them double or treble, nearly 
all have corresponding lines in the solar spectrum. The co- 
incidence is so striking that it seems hardly possible to avoid 



THE SPECTROSCOPE. 233 

the conclusion that a considerable part of the violet light of 
the sun's spectrum arises from glowing oxygen in the photo- 
sphere. 

What gives especial interest to this investigation by Dr. 
Draper is that it affords the first evidence which science has 
found of the existence of oxygen in the sun, the dark lines 
which would be produced by that substance having been 
looked for in vain. It would seem either that the capacity of 
oxygen for absorbing light selectively is very small, or that it 
exists in the sun only at a very high temperature. 

The reason why these lines are brought out here when they 
are not found in other parts of the spectrum is to be found 
in the extreme faintness of the violet part of the continuous 
spectrum, whereby the bright lines are not obscured by the 
dazzling brilliancy of the background of continuous spectrum. 
If it be asked why these bright lines have not been noticed 
before, the answer is, that the dark lines are here so broad 
and numerous as to cut up the continuous spectrum into very 
narrow lines of very irregular brightness, besides which ab- 
sorption bands or half shades are numerous. Again, the lines 
of oxygen do not appear to be so narrow and sharply defined 
as those of the metallic vapors, and this makes it more diffi- 
cult to distinguish them from spaces between the dark bands. 

The reader now understands that when the light from a ce- 
lestial object is analyzed by the prism, and the component col- 
ors are spread out singly as on a sheet, the dark and bright 
lines which we see are the letters of the open book which we 
are to interpret so as to learn what they tell us of the body 
from which the light came, or the vapors through which it 
passed. When we see a line or a set of lines which we rec- 
ognize as produced by a known substance, we infer the pres- 
ence of that substance. The question may now be asked, How 
do we know but that the lines we observe may be produced 
by other substances besides those which we find to produce 
them in our laboratories ? May not the same lines be pro- 
duced by different substances ? This question can be an- 
swered only by an appeal to probabilities. The evidence in 



23± PllACTICAL ASTRONOMY. 

the case is much the same as that by which, recognizing the 
picture of a friend, we conclude that it is not the picture of 
any one else. For anything we can prove to the contrary, 
another person might have exactly the same features, and 
might, therefore, make the very same picture. But, as a mat- 
ter of fact, we know that practically no two men whom we 
have ever seen do look exactly alike, and it is extremely im- 
probable that they ever would look so. The case is the same 
in spectrum analysis. Among the great number of substances 
which have been examined with the spectroscope, no two give 
the same lines. It is therefore extremely improbable that a 
given system of bright lines could be produced by more than 
one substance. At the same time, the evidence of the spec- 
troscope is not necessarily conclusive in all cases. Should 
only a single line of a substance be found in the spectrum of 
a star or nebula, it would hardly be safe to conclude from that 
alone that the line was really produced by the known sub- 
stance. Collateral evidence might, however, come in. If the 
same line were found both in the sunlight and in that of a 
great number of stars, we should be justified in concluding 
that the lines were all produced by the same substance. All 
we can say in doubtful cases is, that our conclusions must be 
drawn with care and discrimination, and must accord with the 
probabilities of each special case. 



PART III. — THE SOLAR SYSTEM. 



CHAPTER I. 

GENERAL STRUCTURE OF THE SOLAR SYSTEM. 

Having, in the preceding parts, described the general struct- 
ure of the universe, and the methods used by astronomers in 
measuring the heavens and investigating the celestial motions, 
we have next to consider in detail the separate bodies which 
compose the universe, and to trace the. conclusions respecting 
the general order of creation to which this examination may 
lead us. Our natural course will be to begin with a general 
description of the solar system to which our earth belongs, 
considering, first, the great central body of that system, then 
the planets in their order, and, lastly, such irregular bodies as 
comets and meteors. 

We have shown in the first part that the solar system was 
found by Copernicus, Kepler, and Newton to consist of the 
sun, as the great central body, with a number of planets re- 
volving around it in ellipses, having the sun in one of their 
foci ; the whole beinc; bound together bv the law of universal 
gravitation. Modern science has added a great number of 
bodies, and shown the system to be a much more complex one 
than Xewton supposed. As we now know them, the bodies 
of the system may be classified as follows : 

1. The sun, the great central body ; 

2. A group of four inner planets — Mercury, Venus, the 
Earth, and Mars ; 

3. A swarm of small planets or asteroids revolving outside 
the orbit of Mars (about 175 of them are now known) ; 



236 THE SOLAR SYSTEM. 

4. A group of four outer planets — Jupiter, Saturn, Uranus, 
and Neptune ; 

5. A number of satellites of the planets, 18 being now 
known, of which all but one belong to the group of outer 
planets ; 




Fig. 63.— Kelative size of sun and planets. 

6. An unknown number of comets and meteors, revolving 
in very eccentric orbits. 

The eight planets of groups 2 and 4 are called the major 
planets, to distinguish them from all others, which are smaller 
or less important. 



GENERAL STRUCTURE OF THE SOLAR SYSTEM. 237 

The range of size, distance, and mass among the bodies of 
the system is enormous. Neptune is eighty times as far from 
the sun as Mercury, and Jupiter several thousand times as 
heavy. It is, therefore, difficult to lay down a map of the 
whole system on the same scale. If the orbit of Mercury were 
represented with a diameter of one-fourth of an inch, that of 
Neptune would have a diameter of 20 inches. 

With the exception of Neptune, the distances of the eight 
major planets proceed in a tolerably regular progression, the 
group of small planets taking the place of a single planet in 
the series. The progression is known as the law of Titius, 
from its first proposer, and is as follows : Take the series of 
numbers 0, 3, 6, 12, 24, 48, each one after the second being 
formed by doubling the one which precedes it. Add 4 to 
each of these numbers, and we shall have a series of numbers 
giving very nearly the relative distances of the planets from 
the sun. The following table shows the series of numbers thus 
formed, together witli the actual distances of the planets ex- 
pressed on the same scale, the distance of the earth being 
called 10 : 



Planet. 


N umbers of Titius. 


Actual Distance. 


Envr. 


Mercury 

Venus 

Earth 

Mars 

Minor planets 

Jupiter 


+ 4 = 4 

3 + 4 = 7 

<; + 4 = 10 

12 + 4 = 16 
24 + 4 = 28 

48 + 4 = 52 

96 + 4 = 100 

192 + 4 = 196 

384 + 4 = 388 


3.9 

7.2 

10.0 

15.2 

20 to 35 
52.0 

95.4 
191.9 
300.6 


0.1 

0.2 
0.0 

0.8 

0.0 

4.1; 

4.1 
87.4 


Saturn 


Uranus 


Neptune 





It will be seen that before the discovery of Neptune the 
agreement was so close as to suggest the existence of an actual 
law of the distances. But the discovery of this planet in 1S46 
completely disproved the supposed law ; and there is now no 
reason to believe that the proportions of the solar system are 
the result of any exact and simple law whatever. It is true 
that many ingenious people employ themselves from time to 
time in working out numerical relations between the distances 
of the planets, their masses, their times of rotation, and so on, 



238 THE SOLAR SYSTEM. 

and will probably continue to do so ; because the number of 
such relations which can be made to come somewhere near to 
exact numbers is very great. This, however, does not indicate 
any law of nature. If We take forty or fifty numbers of any 
kind — say the years in which a few persons were born ; their 
ages in years, months, and days at some particular event in 
their lives ; the numbers of the houses in which they live ; and 
so on^-we should find as many curious relations among the 
numbers as have ever been found among those of the planet- 
ary system. Indeed, such relations among the years of the lives 
of great actors in the world's history will be remembered by 
many readers as occurring now and then in the public journals. 
Range of Planetary Masses. — The great diversity of the size 
and mass of the planets is shown by the curious fact, that, con- 
sidering the sun and the eight planets, the mass of each of the 
nine bodies exceeds the combined mass of all those which are 
smaller than itself. This is shown in the following simple cal- 
culation. Suppose the sun to be divided into a thousand mill- 
ions of equal parts, one of which parts we take as the unit of 
weight: then, according to the best determinations yet made, 
the mass of each planet will be that used in the following cal- 
culation, in which each mass is added to the masses of all the 
planets which are smaller than itself, the planets being taken 
in the order of their masses, beginning with the smallest : 

Mass of Mercury 200 

Mass of Mars 339 

Combined mass of Mercury and Mars 539 

Mass of Venus 2,353 

Combined mass of Mercury, Venus, and Mars 2,892 

Mass of the Earth 3,060 

Combined mass of the four inner planets 5,952 

Mass of Uranus 44,250 

Combined mass of five planets 50,202 

Mass of Neptune.. 51,600 

Combined mass of six planets 101,802 

Mass of Saturn 285,580 

Combined mass of seven planets 387,382 

Mass of Jupiter 954,305 

Combined mass of all the planets 1,341,687 

Mass of the sun 1,000,000,000 






ASPECTS OF THE PLANETS. 239 

It will be seen that the combined mass of all the planets is 
less than -^ that of the sun ; that Jupiter is between two and 
three times as heavy as the other seven planets together ; Sat- 
urn more than twice as heavy as the other six ; and so on. 

Aspects of the Planets. — The apparent motions of the plan- 
ets are described in the first chapter of this work ; and in the 
second chapter it is shown how these apparent motions result 
from the real motions as laid down by Copernicus. The best 
time to see one of the outer planets is when in opposition to 
the sun. It then rises at sunset, and passes the meridian at 
midnight. Between sunset and midnight it will be seen some- 
where between east and south. During the three months fol- 
lowing the day of opposition, the planet will rise from three 
to six minutes earlier every day. A month after opposition, it 
will be two to three hours high soon after sunset, and will | 
the meridian between nine and ten o'clock at night ; while 
three months after opposition, it will be on the meridian about 
six in the evening. Hence, knowing when a planet is in op- 
position, a spectator will know pretty nearly where to look for 
it. His search will be facilitated by the use of a star map 
showing the position of the ecliptic among the stars, because 
the planets are always very near the ecliptic. Indeed, if any 
bright star is not down on the map, he may feel sure that it is 
a planet. 

In describing the individual planets, we give the times when 
they are in opposition, so that the reader may always be able 
to recognize them at favorable seasons, if he wishes to do so. 

The arrangement of the planets, with their satellites, is as 
follows : 



Innee Geocp.. 



f Mercury. 
J Venus. 

J Earth, with its moon. 
I Mars, with 2 moons. 

The minor planets, or asteroids. 

f Jupiter, with 4 moons. 
Outer Group ok J Saturn, with rings and 8 moons. 
Geeat Planets, j TJranus, with 4 moons. 

I Neptune, with 1 moon. 

17 



240 



THE SOLAR SYSTEM. 



This arrangement is partly exhibited in the following plan 
of the solar system, showing the relations of the planetary or- 
bits from the earth outward. The scale is too small to show 
the orbits of Mercury aild Venus. 

Mt2t-g eptupe - 



o ^t__of_5££nu 




Fig. 64.— Orbits of the planets from the earth outward, showing their relative distances 
from the sun in the centre. The positions of the planets are near those which they oc- 
cupy in 1877. 



THE PHOTOSPHERE. 241 



CHAPTER IT. 

THE SUN. 

The sun presents to our view the aspect of a brilliant globe 
32', or a little more than half a degree, in diameter. To give 
precision to our language, the shining surface of this globe, 
which we see with the eye or with the telescope, and which 
forms the visible sun, is called the photosphere. Its light ex- 
ceeds in intensity any that can be produced by artificial 
means, the electric light between charcoal points being the 
only one which does not look absolutely black against the un- 
clouded sun. Our knowledge of the nature of this luminary , 
commences with the invention of the telescope, since without 
this instrument it was impossible to form any conception of 
its constitution. The ancients had a vague idea that it was a 
globe of fire, and in this they were more nearly right than 
some of the moderns ; but there was so entire an absence of 
all real foundation for their opinions that the latter are of lit- 
tle interest to any one but the historian of philosophy. We 
shall, therefore, commence our description of the sun with a 
consideration of the telescopic researches of recent times. 

§ 1. The Photosphere. 

To the naked eye the photosphere, or shining surface of the 
sun, presents an aspect of such entire uniformity that any at- 
tempt to gain an insight into its structure seems hopeless. 
But when we apply a telescope, we generally find it diversified 
with one or more groups of dark-looking spots ; and if the vis- 
ion is good, and w T e look carefully, we shall soon see that the 
whole bright surface presents a mottled appearance, looking 
like a fluid in which ill-defined rice-grains are suspended. Per- 
haps the most familiar idea of this appearance will be pre- 



242 THE SOLAR SYSTEM. 

sented by saying that the sun looks like a plate of rice soup, 
the grains of rice, however, being really hundreds of miles in 
length. Some years ago Mr. Nasmyth, of England, examining 
the sun with high telescopic powers, announced that this mot- 
tled appearance seemed to him to be produced by the inter- 
lacing of long, narrow objects shaped like willow leaves, w\hich, 
running and crossing in all directions, form a net-work, cover- 
ing the entire photosphere. This view, though it has become 
celebrated through the very great care which Mr. Nasinyth 
devoted to his observations, has not been confirmed by subse- 
quent observers. 

Among the most careful and laborious telescopic studies of 
the sun recently made are those of Professor Langley.* He 
has a fine telescope at his command, in a situation where the 
air seems to be less disturbed by the sun's rays than is usual 
in other localities. According to his observations, when the 
sun is carefully examined, the mottling which we have de- 
scribed is seen to be caused by an appearance like fleecy 
clouds whose outlines are nearly indistinguishable. We may 
also discern numerous faint dots on the white background. 
Under high powers, used in favorable moments, the surface 
of any one of the fleecy patches is resolved into a congeries 
of small, intensely bright bodies, irregularly distributed, which 
seem to be suspended in a comparatively dark medium, and 
whose definiteness of size and outline, though not absolute, is 
yet striking, by contrast with the vagueness of the cloud-like 
forms seen before, and which we now perceive to be due to 
their aggregation. The " dots " seen before are considerable 
openings, caused by the absence of the white nodules at cer- 
tain points, and the consequent exposure of the gray medium 
which forms the general background. These openings have 
been called pores. Their variety of size makes any measure- 
ments nearly valueless, though we may estimate in a very 
rough way the diameter of the more conspicuous at from 2" 
to 4". 

* Professor S. P. Langley, Director of the Observatory at Allegheny, Pennsyl- 
vania. 



THE PHOTOSPHERE. 243 

In moments when the definition is very fine, the bright nod- 
ules or rice-grains are found to be made up of clusters of mi- 
nute points of light or "granules," about one-third of a second 
in diameter. These have also been seen around the edges of 
the pores by Secchi, who estimated their magnitude as even 
less than that assigned by Langley. The fact that these points 
are aggregated into little clusters, which ordinarily present the 
appearance of rice-grains, gives the latter a certain irregulari- 
ty of outline which has been remarked by Mr. Huggins. Thus, 
there appear to be three orders of aggregation in the brighter 
.regions of the photosphere : cloud-like forms which can be 
easily seen at any time ; rice-grains or nodules, into which these 
forms are resolved, and which can always be seen with a fair 
telescope under good definition; and granules which make up 
the rice-grains. There is, however, no sharp distinction to be 
drawn between the nodules and the rice-grains : it might be 
almost as near the truth to say that the rice-grains are of va- 
rious sizes, ranging from one-third of a second in diameter to 
one second or more, and that the smaller ones are often col- 
lected into minute clusters, which can hardly be distinguished 
from grains of larger size. 

Yet more recent are the studies of the sun's surface made 
by Janssen,* of France, with the aid of photography. This 
method has a great advantage in the strength and perma- 
nency of the photographic record, and the consequent power 
of studying it at leisure. A disadvantage arises from the 
great foe of astronomical observation which we have already 
described — atmospheric undulations, which render the sun's 
image tremulous and confused except at occasional moments. 
This difficulty may, however, be obviated by taking a great 
number of photographs, and selecting those which show the 
best images. 

In applying this method, Janssen has taken his photographs 
on a larger scale than has been attempted by his predecessors, 
his largest pictures of the sun being from twelve to fifteen 

* Prof. J. C. Janssen, director of the physical observatory at Meudon, France. 



244 THE SOLAR SYSTEM. 

inches in diameter. The granulation is thus brought out with 
remarkable distinctness, as may be seen from the following 
figure, which is enlarged so that the whole sun, on the same 
scale, would be three feef in diameter. 




Fig. 64a. — Aspect of the Sun's Surface as Photographed by Jansseu at the Observatory 

of Meudon. 

M. Janssen finds that the granular elements are of very dif- 
ferent sizes and brilliancy, the diameters ranging from a few 
tenths of a second to three or four seconds. The form is gen- 
erally slightly elliptic, but is subject to considerable variations. 
The differences of brilliancy among the granules seem to arise 
from their being situated at different depths in the photo- 
sphere. But the most remarkable result of Janssen's photo- 
graphs is what he calls the photospheric net -work, " reseau 
photospherique" This is not a net- work of lines, as we might 
understand it, but a subdivision of the photosphere into regions 
in which the granules look hard and well defined, and regions 
in which they look softened and indistinct. This appearance 
is shown, though somewhat imperfectly, in the above figure, 



THE PHOTOSPHERE. 245 

which is taken from one of Janssen's photographs. The boun- 
daries of the regions of well and ill defined granulations are 
necessarily somewhat indefinite, and sometimes appear straight 
and sometimes curved. The dimensions of the regions of ill- 
defined granulation are very variable. Sometimes they attain 
a diameter of one minute or more. Within them, the granules 
sometimes disappear entirely, their place being occupied by 
streams of matter. This disappearance seems to be due to 
violent movements of the photospheric matter destroying the 
granular elements. 

When we call these shining objects "granules," it must be 
remembered that we speak of the appearance, not of the reali- 
ty. To subtend an angle of one second, at the distance of the 
sun, a line must be 450 miles long ; consequently, from what 
is said of the size of the granules, they must be from 100 to 
500 miles in length and breadth. 

If we carefully examine the sun with a very dark smoked 
glass, we shall find that the disk is brightest at the centre, 
shading off on all sides towards the limb. Careful compari- 
sons of the intensity of radiation of different parts of the disk 
show that this diminution near the limb is common to all the 
rays, whether those of heat, of light, or of chemical action. 
The most recent measures of the heat rays were made by 
Langley by means of a thermo-electric pile, those of the light 
rays by Pickering,* and those of the chemical rays by Vogel.f 
The intensities of these several radiations at different distances 
from the centre of the disk as thus determined are shown in 
the table on the following page. The intensity at the centre 
is always supposed 100. The first column gives the distance 
from the centre in fractions of the sun's radius, which is sup- 
posed unity. Thus, the first line of the table corresponds to 
the centre ; the last to the edge. Professor Langley's meas- 
ures do not, however, extend to the extreme edge. 

* Professor E. C. Pickering, Director of the Harvard Observatory, Cambridge, 
Massachusetts. 

t Dr. Hermann C. Vogel, formerly astronomer at Bothkamp, now of the Solar 
Observatory in Potsdam, Prussia. 



24:6 



THE SOLAR SYSTEM. 



Distance from 


Heat Rays 


Light 


Chemical Rays 


Centre of the Sun. 


(Langley). 


(Pickering). 


(Vogel). 


.00 


100 


100 


100 


.125 




99 


100 


.25 


99 


97 


98 


.875 




94 


95 


.50 


95 


91 


90 


.625 




86 


81 


.75 


86 


79 


66 


.85 




69 


48 


.95 




55 


25 


.96 


62 




23 


.98 


50 




18 


1.00 




37 


13 



It will be seen that near the edge of the disk the chemical 
rays fall off most rapidly, the light rays next, and the heat 
rays least of all. Roughly speaking, each square minute near 
the limb of the sun gives about half as much heat as at the 
centre, about one-third as much light, and less than one-seventh 
as many photographic rays. Of the cause of this degradation 
of light and heat towards the limb of the sun no doubt has 
been entertained since it was first investigated. It is found in 
the absorption of the rays by a solar atmosphere. The sun 
being a globe surrounded by an atmosphere, the rays which 
emanate from the photosphere in a horizontal direction have 
a greater thickness of atmosphere to pass through than those 
which strike out vertically; while the former are those we 
see near the edge of the disk, and the latter near the centre. 
The different absorptions of different classes of rays corre- 
spond exactly to this supposition, it being known that the 
more refrangible or chemical rays are most absorbed by va- 
pors, and the heat rays the least. 

From this it follows that we get but a fraction — perhaps a 
small fraction — of the light and heat actually emitted by the 
sun ; and that if the latter had no atmosphere, it would be 
much hotter, much brighter, and bluer in color, than it actually 
is. The total amount of absorption has been very differently 
estimated by different authorities, Laplace supposing it might 
be as much as eleven - twelfths of the whole amount. The 
smaller estimates are, however, more likely to be near the 



THE PHOTOSPHERE. 247 

truth, there being no good reason for holding that more than 
half the rajs are absorbed. That is, if the sun had no atmos- 
phere, it might be twice as bright and as hot as it actually is, 
but would not be likely to be three or four times so. Profess- 
or Langley suggests that the glacial epoch may have been due 
to a greater absorption of the sun's heat by its atmosphere in 
some past geological age. 

A very important physical and astronomical problem is that 
of measuring the total amount of heat radiated by the sun to 
the earth during any period of time — say a day or a year. 
The question admits of a perfectly definite answer, but there 
are two difficulties in the way of obtaining it; one, to distin- 
guish between the heat coming from the sun itself, and that 
coming from the atmosphere and surrounding objects; the 
other, to allow for the absorption of the solar heat by our at- 
mosphere, which must be done in order to determine the to- 
tal quantity emanating from the sun. The most successful 
experiments for this purpose are those of Pouillet and of 
Sir John Herschel. The results obtained by the former may 
be expressed thus : if the air were out of the way, and a sheet 
of ice were so held that the sun's rays should fall upon it per- 
pendicularly, and be all absorbed, the ice would melt away at 
the rate of 14J inches in 2-i hours. Since the sun is part of 
the time below the horizon, and is not perpendicular to more 
than a single point of the earth's surface when above it, the 
average amount of ice which would be melted over the whole 
earth is only a fraction of this, namely, 3.62 inches per day, 
or something more than 100 feet per year. 

Attempts have been made to determine the temperature of 
the sun from the amount of heat which it radiates, but the 
estimates have varied very widely, awing to the uncertainty 
respecting the law of radiation at high temperatures. By sup- 
posing the radiation proportional to the temperature, Secchi* 
finds the latter to be several million degrees, while, by taking 
another law indicated by the experiments of Dulong and 

* Father Angelo Secchi, Director of the Observatory at Rome. 



248 



THE SOLAR SYSTEM. 



Petit, others find a temperature not many times exceeding 
that of a reverberatory furnace. For the temperature of the 
photosphere, it seems likely that the lower estimates are more 
nearly right, being founded on an experimental law ; but the 
temperature of the interior must be immensely higher. 

, § 2. The Solar Spots and Rotation. 

Even the poor telescopes made by the contemporaries of 
Galileo could hardly be directed to the sun many times with- 
out one or more spots being seen on his surface. Whatever 
credit may be due for a discovery which required neither in- 
dustry nor skill should, by the rule of modern science already 
referred to, be awarded to Fabritius for the discovery of the 
solar spots. This observer, otherwise unknown in astronomy, 
made known the existence of the solar spots early in 1611 — 
a year after Galileo began to scan the heavens with his tel- 
escope. His discovery was followed up by Galileo and Schei- 
ner, by whom the first knowledge of the nature of the spots 
was acquired. 

The first idea of Scheiner was that the spots were small 
planets in the neighborhood of the sun ; but this was speedily 
disproved by Galileo, who showed that they must be on the 
surface of the sun itself. The idea of the sun being affected 
with any imperfection so gross as a dark spot was repugnant 
to the ecclesiastical philosophy of the times, and it is not un- 
likely that Schemer's explanation was suggested by the desire 
to save the perfection of our central luminary. 

A very little observation showed that the spots had a regu- 
lar motion across the disk of the sun from east to west, occu- 
pying about 12 days in the transit. A spot generally appeared 
first on or near the east limb, and, after 12 or 14 days, disap- 
peared at the west limb. At the end of another 14 days or 
more it reappeared at the east limb, unless in the mean time 
it had vanished from sight entirely. The spots were found 
not to be permanent objects, but to come into existence from 
time to time, and, after lasting a few days, weeks, or months, 
to disappear. But so long as they lasted, they always ex- 



THE SOLAR SPOTS AND ROTATION. 



240 



hibited the motion just described, and it was thence inferred 
that the sun rotated on his axis in about 25 days. 

The astronomers of the seventeenth and eighteenth centuries 
used a method of observing the sun which will often be found 
convenient for seeing the spots when one has not a telescope 
supplied with dark glasses at his disposal. Take an ordinary 
good spy-glass, or, indeed, a telescope of any size, and point 




Pig. 65.— Man holding telescope, to show sun on screen. 

it at the sun. To save the eyes, the right direction may be 
found by holding a piece of paper closely in front of the eye- 
piece : when the sun shines through the telescope on this pa- 
per, the pointing is nearly right. The telescope should be at- 
tached to some movable support, so that its pointing can be 
changed to the different directions of the sun, and should pass 
through a perforation in some sort of a screen, so that the 
sun cannot shine in front of the telescope except by passing 



250 



THE SOLAR SYSTEM. 



through it. An opening in a window-shutter will answer a 
good purpose, only the rays must not have to pass through the 
glass of the window in order to reach the telescope. Draw 
out the eye-piece of the instrument about the eighth of an 
inch beyond the proper point for seeing a distant object. 
Then, holding a piece of white paper before the eye-piece at 
a distance of from 6 to 12 inches, an image of the sun will be 
thrown upon it. The distance of the paper must be adjusted 
to the distance the eye-piece is drawn out. The farther we 
draw out the eye - piece, the nearer the best image will be 
formed. Having adjusted everything so that the edge of the 
sun's image shall be sharply defined, one or more spots can 
generally be seen. This method, or something similar to it, is 
often used in observing eclipses and transits of Mercury, and 
is very convenient when it is desired 'to show an enlarged im- 
age of the sun to a number of spectators. 

When powerful telescopes were applied to the sun, it was 
found that the spots were not merely the dark patches which 
they first appeared to be, but that they comprised two well- 




Fig. 6C— Solar spot, after Secchi. 

marked portions. The central part, called the umbra or nu- 
cleus, is the darkest, and is surrounded by a border, interme- 
diate in tint between the darkness of the spot and the brill- 



THE SOLAR SPOTS AND ROTATION. 251 

iancy of the solar surface. This border is termed the penum- 
bra. Ordinarily it appears of a uniform gray tint. But when 
carefully examined with a good telescope in a very steady at- 
mosphere, it is found to be striated, looking, in fact, much like 
the bottom of a thatched roof, the separate straws being di- 
rected towards the interior of the spot. This appearance is 
shown in the figure. 

The spots are extremely irregular in form and unequal in 
size. They are very generally seen in groups — sometimes 
two or more combined into a single one ; and it frequently 
happens that a large one breaks up into several smaller ones. 
Their duration is also extremely variable, ranging from a few 
days to periods of several months. 

Until about a century ago, it was a question whether the 
spots were not dark patches, like scoria, floating on the molten 
surface of the photosphere. Wilson, a Scotch observer, how- 
ever, found that they appeared like cavities in the photosphere, 
the dark part being really lower than the bright surface around 
it. As a spot approached the edge of the disk, he found that 
the penumbra grew disproportionately narrow on the side 
nearest to the sun's centre, showing that this side of it was 
seen at a smaller angle than the other. This effect of per- 
spective is shown in Fig. 67, where, near the sun's limb, the 
side of the penumbra nearest us is hidden by the photosphere. 
That the spots are cavities is also shown by the fact that 
when a large spot is exactly on the edge of the disk a notch 
is sometimes seen there. The shaded penumbra seems to 
form the sides of the cavity, while the umbra is the invisible 
bottom. 

These observations gave rise to the celebrated theory of 
Wilson, which is generally connected with the name of Her- 
schel, who developed it more fully. The interior of the sun 
is, by this theory, a cool, dark body, surrounded by two layers 
of clouds. The outer layer is intensely brilliant, and forms 
the visible photosphere, while the inner layer is darker, and 
forms the umbra around the spots. The latter are simply 
openings through these clouds, which form from time to 



252 



TEE SOLAR SYSTEM. 




Fig. 67 — Changes in the aspect of a solar spot as it crosses the sun's disk, showing it to be 
a cavity in the photosphere. 

time, and through which we see the dark body in the interior. 
Anxious that this body should serve some especial purpose in 
the economy of creation, they peopled it with intelligent be- 
ings, who were protected from the fierce radiation of the pho- 
tosphere by the layer of cool clouds, but were denied every 
view of the universe without, except such glimpses as they 
might obtain through the occasional openings in the photo- 
sphere, which we see as spots. 

Leaving out the fancy of living beings, this theory account- 
ed very well for appearances. That the photosphere could not 
be absolutely and wholly solid, liquid, or gaseous seemed evi- 
dent from the nature of the spots. If it were solid, the latter 
could not be in such a constant state of change as we see 



THE SOLAR SPOTS AND ROTATION. 253 

them ; while if it were liquid or gaseous, these cavities could 
not continue for months, as they were sometimes seen to, be- 
cause the liquid or gaseous matter would rush in from all 
sides, and till them up. The only hypothesis that seemed left 
open to Herschel was that the photosphere consisted of clouds 
floating in an atmosphere. As the sides of the cavities looked 
comparatively dark, the conclusion seemed inevitable that the 
brilliancy of the photosphere was only on and near the sur- 
face; and as the bottom of the cavity looked entirely dark, 
the conclusion that the sun had a dark interior seemed una- 
voidable. 

The discovery of the conservation of force, and of the mut- 
ual convertibility of heat and force, was fatal to this theory. 
Such a sun as that of Herschel would have cooled off entirely in 
a few days, and then we should receive neither light nor heat 
from it. A continuous flood of heat such as the sun has been 
radiating for thousands of years can be kept up only by a con- 
stant expenditure of force in some of its forms ; but, on Her- 
schel's theory, the supply necessary to meet this expenditure 
was impossible. Even if the heat of the photosphere could 
be kept up by any agency, it would be constantly conveyed to 
the interior by conduction and radiation ; so that in time the 
whole sun would become as hot as the photosphere, and its 
inhabitants would be destroyed. In the time of Herschel it 
was not deemed necessary that the sun should be a very hot 
body, the heat received from his rays being supposed by many 
to be generated by their passage through our atmosphere. 
The photosphere was, therefore, supposed to be simply phos- 
phorescent, not hot. This idea is still entertained by many 
educated men w T ho have not made themselves acquainted with 
the laws of heat discovered during the present century. We 
may, therefore, remark that it is completely untenable. One 
of the best established results of these laws is that the surface 
of the sun is intensely hot, probably much hotter than any re- 
verberatory furnace. The great question in the present state 
of science is, how the supply of heat is maintained against 
such immense loss by radiation. 



254 THE SOLAR SYSTEM. 

§ 3. Periodicity of the Spots. 

The careful observations of the solar spots which have been 
made during the last century seem to indicate a period of 
about eleven years in the spot-producing activity of the sun. 
During two or three years the spots are larger and more nu- 
merous than on the average; they then begin to diminish, 
and reach a minimum five or six years after the maximum. 
Another six years brings the return of the maximum. The 
intervals are, however, somewhat irregular, and further obser- 
vations are required before the law of this period can be fixed 
with certainty. An idea of the evidence in favor of the pe- 
riod may be formed from some results of the observations of 
Schwabe, a German astronomer, who systematically observed 
the sun during a large part of a long life. One of his meas- 
ures of the spot-producing power was the number of days on 
which he saw the sun without spots in the course of each 
year. The following are some of his results : 

From 1828 to 1831, sun without spots on only 1 day. 

In 1833, " " " 139 days. 

From 1836 to 1840, " " " 3 days. 

In 1843, " " " 147 days. 

From 1847 to 1851, " " " 2 days. 

In 1856, " " " 193 days. 

From 1858 to 1861, " " " no day. 

In 1867, " " " 195 days. 

We see that the sun was remarkably free from spots in the 
years 1833, 1843, 1856, and 1867, about half the time no con- 
siderable spot being visible. This recurrence of the period 
has been traced back by Dr. Wolf, of Zurich, to the time of 
Galileo, and its average length is about 11 years 1 month. 
The years of fewest sun-spots during the present century were 
1810, 1823, 1833, 1844, 1856, and 1867. Continuing the 
series, we may expect very few spots in 1878, 1889, etc. The 
years of greatest production of spots were 1804, 1816, 1829, 
1837, 1848, 1860, and 1870, from which we may conclude 
that 1882, 1893, etc., will be years of numerous sun-spots. 



PERIODICITY OF THE SPOTS. 255 

The observations of Scliwabe and the researehes of Wolf 
seem to have placed the existence of this period beyond a 
doubt; but no satisfactory explanation of its cause has yet 
been given. When first noticed, its near approach to the pe- 
riod of revolution of Jupiter naturally led to the belief that 
there was a connection between the two, and that the attrac- 
tion of the largest planet of the system produced some disturb- 
ance in the sun, which was greater in perihelion than in aphe- 
lion. But this connection seems to be disproved by the fact 
that the sun-spot period is at least six months, and perhaps a 
year, shorter than the revolution of Jupiter. It is therefore 
probable that the periodicity in question is not due to any ac- 
tion outside the sun, but is a result of some law of solar action 
of which we are as yet ignorant. 

There are certain supposed connections of the sun-spot pe- 
riod with terrestrial phenomena which are of interest. Sir 
William Ilerschel collected quite a mass of statistics tending to 
show that there was an intimate connection between the num- 
ber of sun-spots and the price of corn, the latter being low 
when there were few spots, and high when they were more 
numerous. His conclusion was that the fewer the spots, the 
more favorable the solar rays to the growth of the crops. 
This theory has not been confirmed by subsequent observa- 
tion. There is, however, some reason to believe, from the 
researches of Professors Lovering and Loomis, that the fre- 
quency of auroras and of magnetic disturbances is subject to 
a period corresponding to that of sun-spots, these occurrences 
being most frequent when the spots are most numerous. Pro- 
fessor Loomis considers the coincidence to be pretty well 
proved, while Professor Lovering is more cautious, and waits 
for further research before coming to a positive conclusion. 
The occurrence of great auroras in 1859 and 1870-71 was 
strikingly accordant with the theory. 

§4. Law of Rotation of the Sun. 

Between the years 1843 and 1861, a very careful series of 
observations of the positions and motions of the solar spots 

18 



256 THE SOLAR SYSTEM. 

was made by Mr. Carrington, of England, with a view of de- 
ducing the exact time in which the sun rotates on his axis. 
These observations led to the remarkable result that the time 
of rotation shown by the spots was not the same on all parts 
of the sun, but that the equatorial regions seemed to perform 
a revolution in less time than those nearer the poles. Near 
the equator the period was about 25.3 days, while it was a 
day longer in 30° latitude. Moreover, the period of rotation 
seems to be different at different times, and to vary with the 
frequency of the spots. But the laws of these variations are 
not yet established. In consequence of their existence, we 
cannot fix any definite time of rotation for the sun, as we can 
for the earth and for some of the planets. It varies at dif- 
ferent times, and under different circumstances, from 25 to 
26J days. 

The cause of these variations is a subject on which there is 
yet no general agreement among those who have most care- 
fully investigated the subject. Zollner* and Wolf see in the 
general motions of the spots traces of currents moving from 
both poles of the sun towards the equator. The latter con- 
siders that the eleven -year spot -period is associated with a 
flood of liquid or gaseous matter thrown up at the poles of 
the sun about once in eleven years, and gradually finding its 
way to the equator. Zollner adopts the same theory, and has 
submitted it to a mathematical analysis, the basis of which is 
that the sun has a solid crust, over which runs the fluid in 
which the spots are formed. The current springs up near 
the poles, and, starting towards the equator without any rota- 
tion, is acted on by the friction of the revolving crust. By 
this friction the crust continually tends to carry the fluid with 
it. The nearer the current approaches the equator, the more 
rapid the rotation of the crust, owing to its greater distance 
from the axis. The friction acts so slowly that the current 
reaches the equator before it takes up the motion of the crust. 
On this hypothesis, the crust of the sun really revolves in 

* Dr. J. C. F. Zollner, Professor in the University of Leipsic. 



THE SUN'S SURROUNDINGS. 257 

about 25 days ; and the reason that the fluid which covers it 
revolves more slowly at a distance from the sun's equator is 
that it has not yet taken up this normal velocity of rotation. 

This explanation of the seeming paradox that the equatorial 
regions of the sun perform their revolution in a shorter time 
than those parts nearer the poles, cannot be regarded as an es- 
tablished scientific theory. It is mentioned as being, so far as 
the writer is aware, the most completely elaborated explana- 
tion yet offered. It is possible that the spots have a proper 
motion of their own on the solar surface, and that this is the 
reason of the apparent difference in the time of rotation in 
different latitudes. Yet another theory of the subject is that 
of Faye,* who maintains that these differences in the rates of 
rotation are due to ascending and descending currents, as will 
be more fully explained in presenting his views. But w T e here 
touch upon questions which science is as yet far from being 
in a condition to answer. 

§ 5. The Suns Surroundings. 

If the sun had never been examined with any other instru- 
ment than the telescope, nor been totally eclipsed by the inter- 
vention of the moon, we should not have formed any idea of 
the nature of the operations going on at his surface ; but we 
might have been better satisfied that we had a complete knowl- 
edge of his constitution. Indeed, it is remarkable that mod- 
ern science has shown us more mysteries in the sun than it has 
explained ; so that we find ourselves farther than before from 
a satisfactory explanation of solar phenomena. When the an- 
cients supposed the sun to be a globe of molten iron, they had 
an explanation which quite satisfied the requirements of the 
science of their times. The spots were no mystery to Galileo 
and Scheiner, being simply dark places in the photosphere. 
Herschel's explanation of them was quite in accord with the 
science of his time, and he may be regarded as the latest man 
who has held a theory of the physical constitution of the sun 

* Mr. H. E. Fiive, member of the French Academy of Sciences. 



258 THE SOLAR SYSTEM. 

which was really satisfactory at the time it was propounded, 
We have shown how his theory was refuted by the discovery 
of the conservation of force ; we have now to see what per- 
plexing phenomena have been revealed in recent times. 

Phenomena during Total Eclipses. — If, during the progress 
of a total eclipse, the gradually diminishing crescent of the 
sun is watched, nothing remarkable is seen until very near the 
moment of its total disappearance. But, as the last ray of sun- 
light vanishes, a scene of unexampled beauty, grandeur, and im- 
pressiveness breaks upon the view. The globe of the moon, 
black as ink, is seen as if it were hanging in mid-air, surround- 
ed by a crown of soft, silvery light, like that which the old 
painters used to depict around the heads of saints. Besides 
this " corona," tongues of rose-colored flame of the most fan- 
tastic forms shoot out from various points around the edge of 
the lunar disk. Of these two appearances, the corona was no- 
ticed at least as far back as the time of Kepler ; indeed, it was 
not possible for a total eclipse to happen without the specta- 
tors seeing it. But it is only within a century that the at- 
tention of astronomers has been directed to the rose-colored 
flames, although an observation of them was recorded in the 
Philosophical Transactions nearly two centuries ago. They 
are known by the several names of " flames," " prominences," 
and " protuberances." 

The descriptions which have been given of the corona, al- 
though differing in many details, have a general resemblance. 
Halley's description of it, as seen during the total eclipse of 
1715, is as follows: 

"A few seconds before the sun was all hid, there discovered 
itself round the moon a luminous ring about a digit, or per- 
haps a tenth part of the moon's diameter, in breadth. It was 
of a pale whiteness, or rather pearl-color, seeming to me a lit- 
tle tinged with the colors of the iris, and to be concentric 
with the moon." 

The more careful and elaborate observations of recent times 
show that the corona has not the circular form which was for 
inerly ascribed to it, but that it is quite irregular in its out- 



THE SUN'S SURROUNDINGS. 259 

line. Sometimes its form is more nearly square than round, 
the corners of the* square being about 45° of solar latitude, 
and the sides, therefore, corresponding to the poles and the 
equator of the sun. This square appearance does not, how- 
ever, arise from any regularity of form, but from the fact that 
the corona seems brighter and higher half way between the 
poles and the equator of the sun than it does near those points. 




Fig. G8.— Total eclipse of the son as seen at Des Moines. Iowa, August 7th, 1869. Drawn 
by Professor J. R. Eastman. The letters, a, b, c, etc., mark the positions of the prom- 
inences. 

These prominent portions sometimes seem like rays shooting 
out from the sun. The corona is always brightest at its base, 
gradually shading off toward the outer edge. It is impossi- 
ble to say with certainty how far it extends, but there is no 
doubt that it has been seen as far as one semidiameter from 
the moon's limb. 



260 THE SOLAE SYSTEM. 

The corona was formerly supposed to be an atmosphere 
either of the moon or of the sun. Thirty or forty years ago, 
the most plausible theory was that it was a solar atmosphere, 
and that the red protuberances were clouds floating in it. 
That the corona could be a lunar atmosphere was completely 
disproved by its irregular outline, for the atmosphere of a 
body like the moon would necessarily spread itself around in 
nearly uniform layers, and could not be piled up in some 
quarters, as the matter of the corona is seen to be. We shall 
soon see that there is no doubt about the corona being some- 
thing surrounding the sun. 

The question whether the red protuberances belong to the 
moon or the sun was settled during the total eclipse of 1860, 
which was observed in Spain. It was then proved by meas- 
ures of their height above the limb of the moon that the lat- 
ter did not carry them with her, but passed over them. This 
proved that they were fixed relatively to the sun. 

At the time of this eclipse the spectroscope was in its in- 
fancy, and no one thought of applying it to the study of the 
corona and protuberances. The next considerable eclipse oc- 
curred eight years later, in July, 1868, and was visible in In- 
dia and Siam. The spectroscope had, in the mean time, come 
into very general use, and expeditions were despatched from 
several European countries to India to make an examination 
of the spectra of the objects in question. The most success- 
ful observer was Janssen, of France, who took an elevated 
position in the interior, where the air was remarkably clear. 
When, on the eventful day, the last ray of sunlight was cut 
off by the advancing moon, an enormous protuberance showed 
itself, rising to a height of many thousand miles above the sur- 
face of the sun. The spectroscope was promptly turned upon 
it, and the practised eye of the observer saw in a moment that 
the spectrum consisted of the bright lines due to glowing hy- 
drogen. The protuberance, therefore, did not consist of any 
substance shining merely by reflected sunlight, but of an im- 
mense mass of hydrogen gas, so hot as to shine by its own 
light. The theory of the cloud -like nature of the protuber- 
ances was overthrown in a moment. 



THE SUN'S SURROUNDINGS. 261 

This observation marks the commencement of a new era in 
solar physics, which, by a singular coincidence, was inaugu- 
rated independently by another observer. As Janssen looked 
at the lines which he was the first of men to see, it occurred 
to him that they were bright enough to be seen after the total 
phase of the eclipse had passed. He therefore determined to 
watch them, and find how long he could follow them. He 
kept sight of them, not only after the total phase had passed, 
but after the eclipse was entirely over. In fact, he found that 
with a sufficiently powerful spectroscope, he could see the 
spectral lines of the protuberances at any time when the air 
was perfectly clear, so that the varying forms of these remark- 
able objects which had hitherto been seen only during the 
rare moments of a total eclipse could be made a subject of 
regular observation. 

But this great discovery was made in England, independ- 
ently of the eclipse, by Mr. J. Norman Lockyer. This gen- 
tleman was an active student of the subject of spectroscopy ; 
and it had occurred to him that the matter composing these 
protuberances, being so near the surface of the sun, must be 
hot enough, not only to shine by its own light, but to be quite 
vaporized, and, if so, its spectrum might be seen by means of 
the spectroscope. Finding that the instrument he possessed 
would show nothing, he ordered a more powerful one. But 
its construction was attended with so much delay that it was 
not ready till October, 1868. On the 20th of that month, he 
pointed it upon the margin of the sun, and found three bright 
lines in the spectrum, two of which belonged to hydrogen. 
Tims was realized an idea which he had formed two years be- 
fore, but which he was prevented from carrying out by the 
want of a suitable instrument. His success was immediately 
communicated to the French Academy of Sciences, the news 
reaching that body on the very day that word was received 
from Janssen, in India, that he had also solved the same prob- 
lem. 

Following up his researches, Mr. Lockyer found that the 
protuberances arose from a narrow envelope surrounding the 



262 



THE SOLAR SYSTEM. 




Fig. 69.— Specimens of solar protuberances, as drawn by Secchi. The bright base in each 
figure represents the chromosphere from which the red flames rise. 

whole surface of the sun, being, in fact, merely elevated por- 
tions of this envelope : that is to say, the sun is surrounded 
by an atmosphere composed principally of hydrogen gas, por- 
tions of which are here and there thrown up in the form of 



THE srs's 8UBB0UNDING8. 263 

enormous tongues of flame, which, however, can never be seen 
except with the spectroscope, or during total eclipses. To this 
atmosphere Mr. Lockyer gave the name of the chromosphere. 
It had previously been seen and recognized by several observ- 
ers during total eclipses, but nothing had been known respect- 
ing its nature. 

The researches which we have described threw no light on 
the question of the corona, an object which seemed to have 
been almost lost sight of in the excitement caused by the dis- 
covery of the gaseous nature of the protuberances. Happily, 
only a year later, on August 7th, 1869, a total eclipse was visi- 
ble in the United States. The shadow of the moon passed 
down the coast of Alaska, then entered into the interior, pass- 
ing over the south-west portion of British America, entered 
the United States in the Territory of Nebraska, and passed over 
Iowa, Illinois, Kentucky, South-western Virginia, and North 
Carolina. This eclipse was observed very extensively by 
American astronomers, Professor Ilarkness, of the Naval Ob- 
servatory, and Professor Young, of Dartmouth College, devot- 
ing especial attention to the spectroscopic observations. These 
observers found that the corona gave a very faint, continuous 
spectrum crossed by a single bright-green line, which was also 
seen in the spectrum of the protuberances. This solitary line 
was again seen during the eclipse of December 21st, 1870, 
in the Mediterranean ; but it has not been certainly identified 
in the spectrum of any known terrestrial substance. There 
are several lines of iron in its neighborhood; but as this line 
stands alone, it does not seem likely that it can arise from the 
vapor of iron. All we can say is, that the substance which 
skives this line, and which seems to be the onlv gaseous ele- 
ment of the corona, is unknown, and may possibly be some gas 
much lighter than hydrogen which has not yet been discovered 
on the earth. 

Continued observations of the spectra of the various gases 
surrounding the sun show a much greater number of lines 
than have ever been seen during total eclipses. Mr. Lockyer 
himself, by diligent observation extending over several years, 



264 THE SOLAR SYSTEM. 

found over a hundred. But the greatest advance in this re- 
spect was made by Professor C. A. Young. In 1871 an astro- 
nomical expedition was fitted out by the Coast Survey, for the 
purpose of learning by actual trial whether any great advan- 
tage would be gained by establishing an observatory on the 
most elevated point crossed by the Pacific Railway. This 
point was Sherman. The spectroscopic part of the expedition 
was intrusted to Professor Young. Although there was a 
great deal of cloudy weather, yet, when the air was clear, far 
less light was reflected from the sky surrounding the sun than 
at lower altitudes, which was a great advantage in the study 
of the sun's surroundings. Professor Young found no less 
than 273 bright lines which he was able to identify with cer- 
tainty. The presence of many known substances, especially 
iron, magnesium, and titanium, is indicated by these lines; 
but there are also many lines which are not known to pertain 
to any terrestrial substance. 

§ 6. Physical Constitution of the Sun. 

Respecting the physical constitution of the sun, there are 
some points which may be established with more or less cer- 
tainty, but the subject is, for the most part, involved in doubt 
and obscurity. Since the properties of matter are the same 
everywhere, the problem of the physical constitution of the 
sun is solved only w T hen we are able to explain all solar phe- 
nomena by laws of physics which we see in operation around 
us. The fact that the physical laws operative on the sun must 
be at least in agreement with those in operation here, is not 
always remembered by those who have speculated on the sub- 
ject. In stating what is probable, and what is possible, in 
the causes of solar phenomena, we shall begin on the outside, 
and go inwards, because there is less doubt about the opera- 
tions which go on outside the sun than about those on his sur- 
face or in the interior. 

As we approach the sun, the first material substance we 
meet with is the corona, rising to heights of five or ten, per- 
haps even fifteen, minutes above his surface, that is, to a height 



PHYSICAL CONSTITUTION OF THE SUN. 265 

of from one to three hundred thousand miles. Of this ap- 
pendage we may say with entire confidence that it cannot be 
an atmosphere in the sense in which that word is commonly 
used, that is, a continuous mass of elastic gas held up by its 
own elasticity. Of the two reasons in favor of this denial, one 
seems to me almost conclusive, the other entirely so. They 
are as follows : 

1. Gravitation on the sun is about 27 times as great as on 
the earth, and any gas is there 27 times as heavy as here. In 
an atmosphere each stratum is compressed by the weight of 
all the strata above it. The result is, that as we go down by 
successive equal steps, the density of the atmosphere increases 
in geometrical progression. An atmosphere of the lightest 
known gas — hydrogen — would double its density every five or 
ten miles, though heated to as high a temperature as is likely 
to exist at the height of a hundred thousand miles above the 
sun's surface. But there is no approximation to such a rapid 
increase in the density of the corona as we go downwards. If 
we suppose the corona to be such an atmosphere, we must 
suppose it to be hundreds of times lighter than hydrogen. 

2. The great comet of 1843 passed within three or four 
minutes of the surface of the sun, and therefore directly 
through the midst of the corona. At the time of nearest ap- 
proach its velocity was 350 miles per second, and it went with 
nearly this velocity through at least 300,000 miles of corona, 
coming out without having suffered any visible damage or 
retardation. To form an idea what would have become of 
it had it encountered the rarest conceivable atmosphere, we 
have only to reflect that shooting-stars are instantly and com- 
pletely vaporized by the heat caused by their encounter with 
our atmosphere at heights of from 50 to 100 miles ; that is, at 
a height where the atmosphere entirely ceases to reflect the 
light of the sun. The velocity of shooting-stars is from 20 to 
40 miles per second. Remembering, now, that resistance and 
heat increase at least as the square of the velocity, what would 
be the fate of a body, or a collection of bodies like a comet, 
passing through several hundred thousand miles of the rarest 



266 THE SOLAE SYSTEM. 

atmosphere at a rate of over 300 miles a second ? And how 
rare must such an atmosphere be when the comet passes not 
only without destruction, but without losing any sensible ve- 
locity ! Certainly so rare as to be entirely invisible, and inca- 
pable of producing any physical effect. 

What, then, is the corona? Probably detached particles 
partially or wholly vaporized by the intense heat to which 
they are exposed. A mere dust - particle in a cubic mile of 
space would shine intensely when exposed to such a flood of 
light as the sun pours out on every body in his neighborhood. 
The difficult question which we meet is, How are these parti- 
cles held up? To this question only conjectural replies can 
be given. That the particles are not permanently held in one 
position is shown by the fact that the form of the corona is 
subject to great variations. In the eclipse of 1869, Dr. Gould 
thought he detected variations during the three minutes the 
eclipse lasted. The three conjectures that have been formed 
on the subject are: 

1. That the matter of the corona is in what we may call a 
state of projection, being constantly thrown up by the sun, 
while each particle thus projected falls down again according 
to the law of gravitation. The difficulty we encounter here is 
that we must suppose velocities of projection rising as high as 
200 miles per second constantly maintained in every region 
of the solar globe. 

2. That the particles thrown out by the sun are held up a 
greater or less time by electrical repulsion. We know that at- 
mospheric electricity plays an active part in terrestrial mete- 
orology ; and if electric action at the surface of the sun is pro- 
portional to those physical and chemical actions which we 
find to give rise to electrical phenomena here on the earth, 
the development of electricity there must be on an enormous 
scale. 

3. That the corona is due to clouds of minute meteors cir- 
culating around the sun in the immediate vicinity of that lu- 
minary. 

As already intimated, none of these explanations is much 



PHYSICAL CONSTITUTION OF THE SUN. 267 

better than a conjecture, though it is quite probable that the 
facts of the case are divided somewhere among them. 

Next inside the corona lies the chromosphere. Here we 
reach the true atmosphere of the sun, rising in general a few 
seconds above his surface, but now and then projected up- 
wards in immense masses which we might call flame, if the 
word were not entirely inadequate to convey any conception 




Fig. 70. — The sun, with its chromosphere and red flames, on July 23d, 1S71, as drawn by 
Secchi. The figures mark the flames, IT in number. 

of the enormous scale on which thermal action is there car- 
ried on. What we call fire and flame are results of burn- 
ing; but the gases at the surface of the sun are already so 
hot that burning is not possible. Hydrogen is the principal 
material of the upper part of the chromosphere ; but, as we 
descend, we find the vapors of a great number of metals, in- 
cluding iron and magnesium. At the base, where the metals 
are most numerous, and the density the greatest, occurs the 
absorption of the solar rays which causes the dark lines in the 



268 THE SOLAR SYSTEM. 

spectrum already described (p. 225). This seems satisfactori- 
ly proved by an observation of Professor Young's during the 
eclipse of 1870, in Spain. At the moment of disappearance 
of the last rays of sunlight, when he had a glimpse of the 
base of the chromosphere, he saw all the spectral lines re- 
versed ; that is, they were bright lines on a dark ground. The 
vapors which absorb certain rays of the light which passes 
through them from the sun then emitted those same rays 
when the sunlight was cut off. 

The most astonishing phenomena connected with the chro- 
mosphere are those outbursts of its matter which form the pro- 
tuberances. The latter are of two classes — the cloud-like and 
the eruptive. The first class presents the appearance of clouds 
floating in an atmosphere ; but as no atmosphere dense enough 
to sustain anything can possibly exist there, we find the same 
difficulty in accounting for them that we do in accounting for 
the suspension of the matter of the corona. In fact, of the 
three conjectural explanations of the corona, two are inadmis- 
sible if applied to the protuberances, since these cloud -like 
bodies sometimes remain at rest too long to be supposed mov- 
ing under the influence of the sun's gravitation. This leaves 
the electrical explanation as the only adequate one yet brought 
forward. The eruptive protuberances seem to be due to the 
projection of hydrogen and magnesium vapor from the region 
of the chromosphere with velocities which sometimes rise to 
150 miles a second. The eruption may continue for hours, or 
even days, the vapor spreading out into great masses thousands 
of miles in extent, and then falling back on the chromosphere. 

Is it possible to present in language any adequate idea of 
the scale on which natural operations are here carried on ? If 
we call the chromosphere an ocean of fire, we must remember 
that it is an ocean hotter than the fiercest furnace, and as deep 
as the Atlantic is broad. If we call its movements hurricanes, 
we must remember that our hurricanes blow only about a hun- 
dred miles an hour, while those of the chromosphere blow as 
far in a single second. They are such hurricanes as, " coming 
down upon us from the north, would, in thirty seconds after 



PHYSICAL CONSTITUTION OF THE SUN. 269 

they had crossed the St. Lawrence, be in the Gulf of Mexico, 
carryings with them the whole surface of the continent in a 
mass, not simply of ruin, but of glowing vapor, in which the 
vapors arising from the dissolution of the materials composing 
the cities of Boston, New York, and Chicago would be mixed 
in a single indistinguishable cloud." When we speak of erup- 
tions, we call to mind Vesuvius burying the surrounding cities 
in lava ; but the solar eruptions, thrown fifty thousand miles 
high, would ingulf the whole earth, and dissolve every organ- 
ized being on its surface in a moment. When the mediaeval 
poets sung, 

" Dies irae, dies ilia 
Solvet Kcclum in favilla," 

they gave rein to their wildest imagination, without reaching 
any conception of the magnitude or fierceness of the flames 

around the sun. 

Of the corona and chromosphere the telescope ordinarily 
shows us nothing. They are visible only during total eclipses, 
or by the aid of the spectroscope. All we see with the eye or 
the telescope is the shining surface of the sun called the pho- 
tosphere, on which the chromosphere rests. It is this which 
radiates both the light and the heat which reach us. The 
opinions of students respecting the constitution of the photo- 
sphere are so different that it is hardly possible to express any 
views that will not be challenged in some quarter. Although, 
a contrary opinion is held by many, we may venture to say 
that the rays of light and heat seem to come, not from a 
gas, but from solid matter. This is indicated by the fact that 
their spectrum is continuous, and also by the intensity of the 
light, which far exceeds any that a gas has ever been made 
to give forth. It does not follow from this that the photo- 
sphere is a continuous solid or crust, since floating particles of 
solid matter will shine in the same way. The general opinion 
has been that the photosphere is of a cloud-like nature ; that 
is, of minute particles floating in an atmosphere of heated gases. 
That it is not continuously solid like our earth seemed to be 
fully shown by the variations and motions of the spots, which 



270 THE SOLAR SYSTEM. 

have every appearance of going on in a fluid or gas. Indeed, 
of late, some of the most eminent physicists regard it as pure- 
ly gaseous, the pressure making it shine like a solid. 

But this theory is attended with a difficulty which has not 
been sufficiently considered. The photosphere is in striking 
contrast to the gaseous chromosphere, in being subject to no 
sensible changes of level. If it were gaseous, as supposed, 
the solid particles having no connection with each other, we 
should expect those violent eruptions which throw up the pro- 
tuberances to carry up portions of it, so that it would now and 
then present an irregular and jagged outline, as the chromo- 
sphere does. But the most refined observations have never 
shown it to be subject to the slightest change of level, or devi- 
ation from perfect rotundity, except in the region of the spots, 
where its continuity seems to be broken by immense chasm- 
like openings. 

The serene immobility of the photosphere, under such vio- 
lent actions around it as we have described, lends some color 
to the supposition that it is a solid crust which forms around 
the glowing interior of the sun, or, at least, that it is composed 
of a comparatively dense fluid resting upon such a crust. The 
latter is the view of Zollner, who considers some sort of an 
envelope between the exterior and the interior of the sun ab- 
solutely necessary to account for the eruptive protuberances. 
He places this solid envelope three or four thousand miles be- 
low the surface of the photosphere. 

Inside the photosphere we have the enormous interior 
globe, 860,000 miles in diameter. The best-sustained theory 
of the interior is the startling one that it is neither solid nor 
liquid, but gaseous; so that our great luminary is nothing 
more than an immense bubble. The pressure upon the inte- 
rior portions of this mass is such as to reduce it to nearly the 
density of a liquid ; while the temperature is so high as to 
keep the substances in a state which is between the liquid and 
the gaseous, and in which no chemical action is possible. The 
strong point in support of this gaseous theory of the sun's in- 
terior is, that it is the only one which explains how the sun's 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN 271 

light and heat are kept up. How it does this will be shown 
in treating of the laws which govern the secular changes of 
the universe at large. 

§ 7. Views of Distinguished Students of the Sun on the Subject 

its Physical Constitution. 

The progress of our knowledge of the sun during the past 
ten years has been so rapid that only those can completely fol- 
low it who make it the principal business of their lives. For 
the same reason, the views respecting the sun entertained by 
those who are en^a^ed in stud vim? it must be modified and 
extended from time to time. The interest which necessarily 
attaches to the physical source of all life and motion on our 
globe renders the author desirous of presenting these views to 
his readers in their latest form ; and, through the kindness oi 
several of the most eminent investigators of solar physics now 
living, lie is enabled to gratify that desire. The following 
statements are presented in the language of their respective 
authors, except that, in the case of Messrs. Secchi and Faye. 
they are translated from the French for the convenience of 
the English reader. It will be noticed that in some minor 
points they differ from each other, as well as from those which 
the author has expressed in the preceding section. Such dif- 
ferences are unavoidable in the investigation of so difficult a 
subject. 

Views of the Rev. Father Secehi. — " For me, as for every one 
else, the sun is an incandescent body, raised to an enormous 
temperature, in which the substances known to our chemists 
and physicists, as well as several other substances still unknown, 
are in a state of vapor, heated to such a degree that its spec- 
trum is continuous, either on account of the pressure to which 
the vapor is subjected, or of its high temperature. This incan- 
descent mass is what constitutes the photosphere. Its limit is 
defined, as in the case of incandescent gases in general, by the 
temperature to which the exterior layer is reduced by its free 
radiation in space, together with the force of gravity exert- 
ed by the body. The photosphere presents itself as composed 

19 



272 THE SOLAB SYSTEM. 

of small, brilliant granulations, separated by a dark net-work. 
These granulations are only the summits of the flames which 
constitute them, and which rise above the lower absorbing 
layer, which forms the net-work, as we shall soon more clearly 
see. 

" Above the photospheric layer lies an atmosphere of a very 
complex nature. At its base are the heavy metallic vapors, 
at a temperature which, being less elevated, no longer permits 
the emission of light with a continuous spectrum, although it 
is sufficient to give direct spectra with brilliant lines, which 
may be observed, during total eclipses of the sun, at its limb. 
This layer is extremely thin, having a depth of only one or 
two seconds of arc. According to the law of absorption laid 
down by Kirchhoff, these vapors absorb the rays of the spec- 
trum from the light of the photosphere which passes through 
them, thus giving rise to the breaks known as the Fraunhofer 
dark lines of the solar spectrum. These vapors are mixed 
with an enormous quantity of hydrogen. This gas is present 
in such a quantity that it rises considerably above the other 
layer, and forms an envelope rising to a height of from ten 
to sixteen seconds, or even more, which constitutes what we 
call the chromosphere. This hydrogen is always mixed with 
another substance, provisionally called helium, which forms the 
yellow line D 3 of the spectrum of the protuberances, and with 
another still rarer substance, which gives the green line 1474 
K. This last substance rises to a much greater elevation than 
the hydrogen ; but it is not so easily seen in the full sun as 
the latter. Probably there is some other substance not yet 
well determined. Thus, the substances which compose this 
solar envelope appear to be arranged in the order of their 
density ; but still without any well-defined separation, the dif- 
fusion of the gases producing a constant mixture. 

" This atmosphere becomes visible in total eclipses in the 
form of the corona. It is very difficult to fix its absolute 
height. The eclipses prove that it may reach to a height 
equal to the solar diameter in its highest portions. 

" No doubt it extends yet farther, and it may well be con- 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 272 

nected with the zodiacal light. The visible layer of this at- 
mosphere is not spherical; it is higher in middle latitudes, 
near forty-five degrees, than at the equator. It is still more 
depressed at the poles. At the base of the chromosphere, 
the hydrogen has the shape of small flames composed of very 
f thin, close filaments which seem to correspond to the granu- 
lations of the photosphere. During periods of tranquillity 
the direction of these filaments is perpendicular to the solar 
surface ; but during periods of agitation they are generally 
more or less inclined, and often directed systematically tow- 
ards the poles. 

"The body of the sun is never in a state of absolute repose. 
The various substances coming together in the interior of the 
body tend to combine, in consequence of their affinity, and 
necessarily produce agitations and interior movements of every 
kind and of great intensity. Hence the numerous crises which 
show themselves at the surface through the elevation of the 
lower strata of the atmosphere by eruptions, and often by act- 
ual explosions. Then the lower metallic vapors are projected 
to considerable heights, hydrogen especially, at an elevation 
visible in the spectroscope (in full sunlight) of one-fourth the 
solar diameter. These masses of hydrogen, leaving the pho- 
tosphere at a temperature higher than that of the atmosphere, 
rise to the superior regions of the latter, remaining suspend- 
ed, diffusing themselves at considerable elevations, and form- 
ing what are called the prominences or protuberances. The 
structure of the hvdro^enous protuberances is entirely si mi- 
lar to that of fluid veins raising themselves from denser layers, 
and diffusing in the more rare ones : but their extreme varia- 
bility, even at the base, and the rapid changes of the place of 
exit and diffusion, prove that they do not pass through any 
orifice in a solid resisting layer. 

" These eruptions are often mixed with colnmns of metallic 
vapors of greater density, which do not attain the elevation 
of the hydrogen, and of which the nature can be recognized 
by the aid of the spectroscope : occasionally we see them fall- 
ing back on the sun in the form of parabolic jets. The most 



27± THE SOLAR SYSTEM. 

common substances are sodium, magnesium, iron, calcium, etc. 
— indeed, the same substances which are seen to form the low, 
absorbing layer of the solar atmosphere, and which by their 
absorption produce the Fraunhofer lines. A rigorous and in- 
evitable consequence of these conditions is the fact that when 
the mass thus elevated is carried by the rotation of the sun 
between the photosphere and the eye of the observer, the ab- 
sorption becomes very sensible, and produces a dark spot on 
the photosphere itself. The metallic absorption lines are 
then really wider and more diffused in this region ; and if 
the elevated mass is high and dense enough, we can even see 
the re-reversal of the lines already reversed ; that is to say, 
we can see the bright lines of the substance itself on the back- 
ground of the spot. This often happens for hydrogen, which 
rises to a great height, and also with sodium and magnesium, 
which metals have the rarest vapors. Here, then, we have the 
origin of the solar spots. They are formed by masses of ab- 
sorbing vapors which, brought out from the interior of the sun, 
and interposed between the photosphere and the eye of the ob- 
server, prevent a large part of the light from reaching our eyes. 
"But these vapors are heavier than the surrounding mass 
into which they have been thrown. They therefore fall by 
their own weight, and, tending to sink into the photosphere, 
produce in it a sort of cavity or basin filled with a darker and 
more absorbing mass. Hence the aspect of a cavity recognized 
in the spots. If the eruption is instantaneous, or of very short 
duration, this vaporous mass, fallen back on the photosphere, 
♦soon becomes incandescent, reheated, and dissolved, and the 
spot rapidly disappears ; but the interior crises of the body of 
the sun may be continued a long time; and the eruption may 
maintain itself in the same place during two or more rotations 
of the sun. Hence the persistence of the spots; for the cloud 
can continue to form so long and so fast as the photosphere 
dissolves it, as happens with the jets of vapor from our vol- 
canoes. The eruptions, when about to terminate, may be re- 
vived and reproduced several times near the same place, and 
give rise to spots very variable in form and position. 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 275 

"The spots are formed of a central region, called the nu- 
cleus, or umbra, and of a surrounding part less dark, called 
the penumbra. The latter is really formed of thin dark veils, 
and of filaments or currents of photospheric matter which 
tend to encroach upon the dark mass. These currents have 
the form of tongues, often composed of globular masses look- 
ing like strings of beads or willow leaves, and evidently are 
only the grains of the photosphere precipitating themselves 
towards the centre of the spot, and sometimes crossing it like 
a bridge. 




Fig. 71.— Illustrating Secchi's theory of solar spots. 

" In each spot we must distinguish three periods of exist- 
ence : the first, of formation ; the second, of rest ; the third, 
of extinction. In the first, the photospheric mass is raised 
and distorted by a great agitation, often in the nature of a 
vortex, which elevates it all around the flowing streams, and 
forms irregular elevations, either without penumbra or with a 
very irregular one. These irregular movements defy descrip- 
tion : their velocities are enormous, and the agitated region 



276 THE SOLAR SYSTEM. 

extends itself over several square degrees; but this upturn- 
ing soon comes to an end, and the agitation slowly subsides, 
and is succeeded by calm. In the second period, the agi- 
tated and elevated mass falls back again, and tends to com- 
bine in masses more or less circular, and to sink by its weight 
into the surface of the photosphere. Hence the depressed 
form of the photosphere, resembling a funnel, and the numer- 
ous currents which come from each point of the circumference 
to rush upon this obscure mass ; but at the same time the con- 
trast between it and the substance issuing still persists. The 
spot takes a nearly stable and circular form, a contrast which 
may last a long time — so long, in fact, as the interior actions of 
the solar globe furnish new materials. At length, the latter 
ceasing, the eruptive action languishes and is exhausted, and 
the absorbing mass invaded on all sides by the photosphere is 
dissolved and absorbed, and the spot disappears. 

"The existence of these three phases is established by the 
comparative study of the spots and eruptions. When a spot 
is on the sun's border during its first period, although the 
dark region is invisible, its position is indicated by eruptions 
of metallic vapors, if the spot be considerable. On the dark- 
est ones the vapors of sodium, iron, and magnesium are seen 
in the greatest quantity, and raised to great heights. A calm 
and circular spot is crowned by beautiful faculse and jets of 
hydrogen and metallic vapors, very low, though quite brilliant. 
A spot which is on the point of closing up has no metallic 
jets, and at the utmost only a few small jets of hydrogen, and 
a more agitated and elevated chromosphere. Besides, obser- 
vation teaches that the eruptions in general accompany the 
spots, and that they are deficient at times when the spots are 
wanting. Thus the solar activity is measured by the double 
activity of eruptions and spots which have a common source, 
and the spots are really only a secondary phenomenon, de- 
pending upon the eruptions and the more or less absorbing 
quality of the materials : if the erupted materials were not 
absorbent, we could see no spots at all. 

" The eruptions composed simply of hydrogen do not pro- 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. 2 



< • 



duce spots; thus they are seen on all points of the disk, while 
the spots are limited to the tropical zones, where alone the 
metallic eruptions appear. The eruptions of simple hydrogen 
give rise to the facul«3. The greater brilliancy of the faculae 
is due to two causes: the first is, the elevation of the photo- 
sphere above the absorbing stratum of vapor which is very 
thin (only one or two seconds of arc, as we have before said | : 
this elevated region thus escapes the absorption of the lower 
stratum, and appears more brilliant. The other cause may be 
that the hydrogen, in coming out, displaces the absorbing 
stratum, and, taking the place of the metallic vapors, permits 
a better view of the light of the photosphere itself. 

"Thus, in conclusion, the spots are a secondary phenomenon, 
but, nevertheless, inform us of the violent crises which pre- 
vail in the interior of the radiant globe. The frequency of 
the spots corresponding to the frequency of eruptions, the two 
phenomena, taken in connection, are the mark of solar activ- 
ity. The spots occupy the zones on each side of the solar 
equator, and rarely pass beyond the parallel of thirty degrees. 
One or two seen at forty-five degrees are exceptions. That 
parallel is therefore the limit of greate>t activity of the body. 
It is remarkable that the parallels of thirty degrees divide the 
hemispheres into two sectors of equal volume. Beyond these 
parallels we see faculae, but not true spots — or, at most, only 
veiled spots indicative of a very feeble metallic eruption. 

" Such a fluid mass, in which the parts are exposed to very 
different temperatures, could not subsist without an interior 
circulation. We do not yet know its laws; but the following 
facts are well enough established : the zones of spots are not 
fixed, but have a progressive motion from the equator towards 
the poles. The spots, arrived at a certain high latitude, cease 
to appear, but after some time reappear at lower latitudes, 
and afterwards go on anew. Between these phases of dis- 
placement there is commonly a minimum of spots. During 
periods of activity the protuberances have a dominant direc- 
tion towards the pole, as also the flames of the chromosphere. 
This indicates a general movement of the photosphere from 



27S THE SOLAE SYSTEM. 

the equator to the poles. This movement is supported by the 
displacement of the zones of eruption and of the protuber- 
ances, which always seem to move towards the poles. 

" Besides this movement in latitude, the photosphere has 
also a movement in longitude, which is greatest at the equa- 
tor. Thus the time of rotation of the body is different upon 
different parallels, the minimum being at the equator. These 
phenomena lead to the conclusion that the entire mass is af- 
fected with a vortical motion which sets from the equator 
towards the poles, in a direction oblique to the meridians. 
The theory of these movements is still to be elaborated, and 
is, no doubt, connected with the primitive mode in which the 
sun was formed. 

" The activity of the body is subject to considerable fluctu- 
ations : the best established period is one of eleven and one- 
third years, but the activity increases more rapidly than it di- 
minishes — it increases about four years, and diminishes about 
seven. This activity is connected with the phenomena of ter- 
restrial magnetism, but we cannot say in what way. We may 
suppose a direct electro-magnetic influence of the sun upon 
our globe, or an indirect influence due to the thermal action 
of the sun, which reacts upon its magnetism. It is, indeed, 
very natural to suppose that the ethereal mass which fills the 
spaces of our planetary system may be greatly altered and 
modified by the activity *of the central body. But, whatever 
may be the cause of these changes of activity, we are com- 
pletely ignorant of them. The action of the planets has been 
proposed as plausible, but it is far from being satisfactory. 
The true explanation is reserved for the science which shall 
reveal the nature of the connection which unites heat to elec- 
tricity, to magnetism, and to the cause of gravity. 

" Of the interior of the sun we have no certain information. 
The superficial temperature is so great, notwithstanding the 
continual loss of heat which it suffers, that we cannot suppose 
it less in the interior ; and, consequently, no solid layer can ex- 
ist there, except perhaps at depths where the pressure due to 
gravity equals or surpasses the molecular dilatation produced 



VIEWS ON THE PHYSICAL COXSTITUTIOX OF TnE SIX. 27 f J 

by temperature. However it may be, the layer accessible to 
the exploration of our instruments is, no doubt, fluid and gase- 
ous, and we can thus explain the variations of the solar diam- 
eter established by certain astronomers. Notwithstanding" these 
small fluctuations, the radiation of the body into its planetary 
system is nearly constant during widely separated periods, and 
especially is it so during the historic period. This constancy 
is due to several causes : first, to the enormous mass of the 
body, which can be cooled only very slowly, owing to its very 
high temperature; second, to the contraction of the n. 
which accompanies the condensation consequent upon the loss 
of heat; third, to the emission of the heat of dissociation due 
to the production of chemical actions which may take place 
in the total mass. 

" The origin of this heat is to be found in the force of grav- 
ity; for it is well proved that the solar mass, by contracting 
from the limits of the planetary system to its present volume, 
would produce, not only its actual temperature, but one sev- 
eral times greater. As to the absolute value of this tempera- 
ture, we cannot fix it with certainty. Science not yet having 
determined the relation which exists between molecular liv- 
ing force (vis viva) and the intensity of radiation to a distance 
(which last is the only datum given by observation), we find 
ourselves in a state of painful uncertainty. Nevertheless, this 
temperature must be several million degrees of our thermom- 
eter, and capable of maintaining all known substances in a 
state of vapor. 

"Rome, February 11th, 1877." 

Views of M. Faye. — " In studying without any prepossession 
the movements of the spots, we find, with Mr. Carrington, that 
there exists a simple relation between their latitude and their 
angular velocity. Nevertheless, this law does not suffice to 
represent the observations with the exactitude which they ad- 
mit of. It is still necessary to take account by calculation of a 
parallax of depth which I estimate at -j^o of the radius of the 
sun, and of certain oscillations of very small extent, and of 
long period, which the spots undergo perpendicular to their 



2S0 THE SOLAR SYSTEM. 

parallels. Then the observations are represented with great 
precision, from which I conclude that we have to deal with a 
quite simple mechanical phenomenon. The law in question 
can be expressed by the formula, 

i to — a— b sin 2 A; 
w being the angular velocity of a spot at the latitude X, and a 
and b being constants, having the same value (a=857 / .6 and 
&=157'.3) over the whole surface of the sun. These constants 
may vary slowly with the time, but I have not studied their 
variations. 

"Admitting, as we shall see farther on, that the velocity of 
a spot is the same as the mean velocity of that zone of the 
photosphere in which it is formed, we see : 

"1. That the contiguous strips of the photosphere are ani- 
mated with a velocity of rotation nearly constant for each fila- 
ment, at least during a period of several months or years, but 
varying with the latitude from one strip to another. 

" 2. That these strips move nearly parallel to the equator, 
and never give indications of currents constantly directed tow- 
ards either pole, as in the upper regions of our atmosphere. 

" 3. That the spots are hollow, or at least that the black nu- 
cleus is perceptibly depressed in respect to the photosphere. 

" The diminution in the rate of superficial rotation, more 
and more marked towards the poles, and the absence of all 
motion from the equator, can only proceed from the vertical 
ascent of materials rising incessantly from a great depth tow- 
ards all points of the surface. It is sufficient that this depth 
goes on increasing from the equator towards the poles, follow- 
ing a law analogous to that of the rotation, in order that it 
may produce at the surface a retardation increasing with the 
latitude. This retardation is about two days in each rotation 
at forty-five degrees of latitude. The mass of the sun, being 
formed principally of metallic vapors condensable at a certain 
temperature, and that temperature being reached at a certain 
level in consequence of the exterior cooling, there ought to be 
established a double vertical movement of ascending vapors, 
which go to form a cloud of condensed matter susceptible of 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE 8UN. 281 

intense radiation, and of condensed products which fall back 
in the form of rain into the interior. The latter are stopped 
at the depth at which they meet a temperature high enough 
to vaporize them anew, and afterwards force them to reasceud. 
As almost the entire mass of the sun partakes of this double 
movement, the heat radiated by the cloud will be borrowed 
from this mass, and not from a superficial layer, the tempera- 
ture of which would rapidly fall, and which would bood con- 
dense into a complete crust. Hence the formation ami sup- 
port of the photosphere, and the constancy and long duration 
of its radiation, which is also partly fed by the slow contrac- 
tion of the whole mass of the sun. 

u The contiguous bands of the photosphere being animated 
with different velocities, there results a multitude of circular 
gyratory movements around a vertical axis extending to a 
great depth, as in our rivers and in the great upper currents 
of our atmosphere. These whirlpools, which tend to equalize 
the differences of velocity just spoken of, follow the currents 
of the photosphere in the same way that whirlpools, and the 
whirlwinds, tornadoes, and cyclones of our atmosphere follow 
the upper currents in which they originate. Like these, they 
are descending, as I have proved (against the meteorologists) 
by a special study of these terrestrial phenomena. They carry 
down into the depths of the solar mass the cooler materials <>f 
the upper layers, formed principally of hydrogen, and thus 
produce in their centre a decided extinction of light and heat 
as long as the gyratory movement continues. Finally, the 
hydrogen set free at the base of the whirlpool becomes re- 
heated at this great depth, and rises up tumultuously around 
the whirlpool, forming irregular jets which appear above the 
chromosphere. These jets constitute the protuberances. 

"The whirlpools of the sun, like those on the earth, are of 
all dimensions, from the scarcely visible pores to the enormous 
spots which we see from time to time. They have, like those 
of the earth, a marked tendency first to increase, and then to 
break up, and thus form a row of spots extending along the 
same parallel. The penumbra is due to a portion of the photo- 



2 82 THE SOLAR SYSTEM. 

sphere which forms around their conical surface at a lower 
level, on account of the lowering of the temperature produced 
by the whirlpool. Sometimes in this sort of luminous sheath we 
see traces of the whirling movement going on in the interior. 

" It is more difficult to account for the periodicity of the 
spots. It seems to me that it must depend upon fluctuations in 
the form of the interior layer, to which the condensed matter 
of the photosphere falls in the form of rain. This flow of 
materials from above must alter, little by little, the velocity 
of rotation of this layer. If its compression is changed in the 
course of time, and if it becomes rounder, the variations in 
the superficial velocity of the photosphere, as well as the gyra- 
tory movements, will diminish in intensity and frequency. 

"A time will at length arrive when the vertical movements 
which feed the photosphere will become more and more hin- 
dered. The cooling will then be purely superficial, and the 
surface of the sun will harden into a continuous crust. 

"Paris, February, 1877." 

Vieivs of Professor Young. — " 1. It seems to me almost dem- 
onstrated, as a consequence of the low mean density of the 
sun and its great force of gravity, that the central portions of 
that body, and, in fact, all but a comparatively thin shell near 
the surface, must be in a gaseous condition, and the gases at 
so high a temperature as to remain for the most part dissoci- 
ated from each other, and incapable of chemical interaction. 
Under the influence of the great pressure and high tempera- 
ture, however, their density and viscosity are probably such as 
to render their mechanical behavior more like that of such 
substances as tar or honey than that of air, as we are famil- 
iar with it. 

" 2. The visible surface of the sun, the photosphere, is com- 
posed of clouds formed by the condensation and combination 
of such of the solar gases as are cooled sufficiently by their 
radiation into space. These clouds are suspended in the mass 
of un condensed gases like the clouds in our own atmosphere, 
and probably have, for the most part, the form of approximate- 
ly vertical columns, of irregular cross -section, and a length 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE SUN. g 

many times exceeding their diameter. The liquid and -olid 
particles of which they are made up descend continually, their 
places being constantly supplied by fresh condensation from 
the ascending currents which rise between the cloud-columns. 
From the under-surface of the photosphere there must be an 
immense precipitation of what may be called solar 'rain and 
snow,' which descends into the gaseous core, and by the inter- 
nal heat is re-evaporated, decomposed, and restored to its origi- 
nal gaseous condition ; the heat lost by the surface radiation 
being replaced mainly by the mechanical work due to the 
gradual diminution of the sun's bulk, and the thickening of 
the photosphere. I do not know any means of determining 
the thickness of the photospheric shell, but, from the phenom- 
ena of the spots, judge that it can hardly be less than ten 
thousand miles, and that it may be much more. 

" 3. The weight of the cloud-shell, and the resistance offered 
to the descending products of condensation, act to produce on 
the enclosed gaseous core a constricting pressure, which forces 
the gases upwards through the intervals between the clouds 
with great velocity; so that jets or blasts of heated gas con- 
tinually ascend all over the sun's surface, the same material 
subsequently redescending in the cloud-columns, partly con- 
densed into solid or liquid particles, and partly uncondensed, 
but greatly cooled. It seems also not unlikely that in the up- 
per part of the channels through which the ascending currents 
rush, there may often occur the mixture of different gases 
cooled by expansion to temperatures sufficiently below the 
dissociation point to allow of their explosive combination. 

" 4. The * chromosphere ' is simply the layer of uncondensed 
gases which overlies the photosphere, though separated from 
it by no definite surface. The lower portion of the chromo- 
sphere is rich in all the vapors and gases which enter into the 
sun's composition ; but at a comparatively small height the 
denser and less permanent gases disappear, leaving in the up- 
per regions only hydrogen and some other substances not as 
yet identified. The dark lines of the solar spectrum originate 
mainly in the absorption produced by the denser gases which 



2 $4 THE SOLAR SYSTEM. 

bathe the photospheric clouds, and these metallic vapors are 
only occasionally carried into the upper regions by ascending 
jets of unusual violence. When this occurs, it is almost in- 
variably in connection with a solar spot. The prominences 
are merely heated masses of the hydrogen and other chromo- 
spheric gases, carried to a considerable height by the ascend- 
ing currents, and apparently floating in the ' coronal atmos- 
phere,' which interpenetrates and overtops the chromosphere. 

"5. I do not know what to make of the corona. Its spec- 
trum proves that a considerable portion of its light comes 
from some exceedingly rare form of gaseous matter, which 
cannot be identified with anything known to terrestrial chem- 
istry ; and this gas, whatever it may be, exists at a height of 
not less than a million of miles above the solar surface, con- 
stituting the ' coronal atmosphere.' Another portion of its 
light appears to be simply reflected sunshine. But by what 
forces the peculiar radiated structure of the corona is deter- 
mined, I have no definite idea. The analogies of comets' tails 
and auroral streamers both appear suggestive; but, on the other 
hand, the spectra of the corona, the aurora borealis, the com- 
ets, and the nebulae are all different — no two in the least alike. 

" 6. As to sun-spots, there can be no longer any doubt, I 
think, that they are cavities in the upper surface of the photo- 
sphere, and that their darkness is due simply to the absorbing 
action of the gases and vapors which fill them. It is also cer- 
tain that very commonly, if not invariably, there is a violent 
uprush of hydrogen and metallic vapors all around the outer 
edge of the penumbra, and a considerable depression of the 
chromosphere over the centre of the spot ; probably, also, there 
is a descending current through its centre. As to the cause 
of the spots, and the interpretation of their telescopic details, 
I am unsatisfied. The theory of Faye appears to me, on the 
whole, the most reasonable of all that have yet been proposed ; 
but I cannot reconcile it with the want of systematic rotation 
in the spots, or their peculiar forms. Still, it undoubtedly has 
important elements of truth, and may perhaps be modified so 
as to meet these difficulties. As to the periodicity of the spots, 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE 8UK. 285 

I am unable to think it due in any way to planetary action ; 
at least, the evidence appears to me wholly insufficient as yet ; 
but I have no hypothesis to offer. Nor have I any theory to 
propose to account for the certain connection between disturb- 
ances of the solar surface and of terrestrial magnetism. 

" 7. As to the temperature of the sun's surface, I have no 
settled opinion, except that I think it must be much higher 
than that of the carbon points in the electric light. The esti- 
mates of those who base their calculations on Newton's law of 
cooling, which is confessedly a mere approximation, seem to 
me manifestly wrong and exaggerated ; on tli£ other hand, the 
very low estimates of the French physicists, who base their 
calculations on the equation of Dulong and Petit, seem to me 
hardly more trustworthy, since their whole result depends 
upon the accuracy of a numerical exponent determined by ex- 
periment at low temperatures and under circumstances differ- 
ing widely from those of the sun's surface. The process is an 
unsafe extrapolation. The sensible constancy of the 'solar 
radiation seems to be fairly accounted for on the hypothesis 
of slow contraction of the sun's diameter. 

" 8. I look upon the accelerated motion of the sun's equator 
as the most important of the unexplained facts in solar phys- 
ics, and am persuaded that its satisfactory elucidation will carry 
with it the solution of most of the other problems still pending. 

" Such, in* brief, are my 'opinions;' but many of them I 
hold with little confidence and tenacity, and anxiously await 
more light, especially as regards the theory of the sun's rota- 
tion, the cause and constitution of the spots, and the nature of 
the corona. The only peculiarity in my views lies. I think, 
in the importance I assign to the effects of the descending 
products of condensation, which I conceive to form virtually 
a sort of constricting skin, producing pressure upon the gas- 
eous mass beneath, something as the film of a bubble com- 
presses the enclosed air. To the pressure thus produced I 
ascribe mainly the eruptive phenomena of the chromosphere 
and prominences. 

"Dartmouth College, March, 1877." 



286 THE SOLAS SYSTEM. 

Views of Professor Langley. — "It seems to me that we have 
now evidence on which to pass final adverse judgment on 
views which regard the photosphere as an incandescent liquid, 
or the spots as analogous either to scoriae matter, on the one 
hand, or to clouds above the luminous surface, on the other. 
According to direct telescopic evidence, the photosphere is 
purely vaporous, and I consider these upper vapors to be 
lighter than the thinnest cirri of our own sky. The obser- 
vation of faculse allies them and the whole ' granular ' cloud 
structure of the surface most intimately with chromospheric 
forms, seen by the spectroscope, and associates both with the 
idea of an everywhere-acting system of currents which trans- 
mit the internal heat, generated by condensation, to the sur- 
face, and take back the cold, absorbent matter. This vertical 
circulation goes to a depth, I think, sensible even by compari- 
son with the solar diameter. It coexists with approximately 
horizontal movements observed in what may be called the 
successive upper photospheric strata in the vicinity of spots. 
The spots give evidence of cyclonic action such as could only 
occur in a fluid. Their darkness is due to the presence, in 
unusual depth, of the same obscuring atmosphere which forms 
the gray medium in which the luminous photospheric forms 
seem suspended, and which we here look through, where it 
fills openings in the photospheric stratum, down to regions 
of the solar interior made visible by the dim light of clouds 
of luminous vapor, precipitated in lower strata where the dew- 
point has been altered by changed conditions of temperature 
and pressure. All observation and all legitimate inference 
go to show that the sun is gaseous throughout its mass, though 
by this it is not meant to deny the probable precipitation of 
cooling photospheric vapors in something analogous to rain ; 
a condition perhaps necessary to the maintenance of the equi- 
librium of the interchange of cold and heated matter between 
exterior and interior; nor is it meant that the conditions of a 
perfect fluid are to be expected, where these are essentially 
modified (if by no other cause) by the viscosity due to extreme 
heat. The temperature of the sun is, in my view, necessarily 



VIEWS ON THE PHYSICAL CONSTITUTION OF THE SIX. 287 

much greater than that assigned by the numerous physicists. 
who maintain it to be comparable with that obtainable in the 
laboratory furnace; but we cannot confidently assign any up- 
per limit to it until physics has advanced beyond its present 
merely empirical rules connecting emission and temperature; 
for this, and not the lack of accurate data from physical 
astronomy, is the source of nearly all the obscurity now at- 




Fig. 72.— Solar spot, after Langley. 

tending this important question. No theory of the solar con- 
stitution which is free from some objection has yet been pro- 
posed; but if the master-key to the diverse problems it pre- 
sents has not been found, it is still true, I think, that the one 
which unlocks most is that of M. Faye. 

" Of the potential energy of the sun, we may say that we 
believe it to be sufficient for a supply of the present heat dur- 
ing periods to be counted by millions of years. But what ini- 

20 



288 THE SOLAR SYSTEM. 

mediately concerns us is the constancy of the rate of conver- 
sion of this potential into actual radiant energy, as we receive 
it, for on this depends the uniformity of the conditions under 
which we exist. Now, this uniformity in turn depends on 
the equality of the above-mentioned interchanges between the 
solar surface and the interior, an equality of whose constancy 
we know nothing save by limited experience. The most im- 
portant statement with reference to the sun, perhaps, which 
we can make with certainty is even a negative one. It is 
that we have no other than empirical grounds, in the present 
state of knowledge, for believing in the uniformity of the 
solar radiation in prehistoric periods and in the future." 

" The above remarks, limited as they are, appear to me to 
cover nearly all the points as to the sun's physical constitu- 
tion (outside of the positive testimony of the spectroscope) on 
which we are entitled to speak with confidence, even at the 
present time." 



THE PLANET MERCURY. 



289 



CHAPTER III. 

THE iftNER GROUP OF PLANETS. 

§ 1. The Planet Mercury. 

Mercury is the nearest known planet to the sun, and the 
smallest of the eight large planets. Its mean distance from 
the sun is 40 millions of nf -» fo 

miles, and its diameter about 
one-third that of the earth. 

It was well known to the an- / s* y >^^7~- tT^ 

cients, being visible to the / / C s 

naked eye at favorable times, / / / 

if the observer is not in too i 
high a latitude. The central 
and northern regions of Eu- 
rope are so unfavorably sit- 
uated for seeing it that it is 
said Copernicus died without 
ever having been able to ob- „ 

j. . rp,, ,.~, Fig. 73.— Orbits of the f<mr inner pinnetp, ll- 

tain a view of it. The dim- Iustrating the eccentricity of those of Mereu- 

culty of seeing it arises from ry and Mar& 

its proximity to the sun, as it seldom sets more than an hour 
and a half after the sun, or rises more than that length of 
time before it. Hence, when the evening is sufficiently ad- 
vanced to allow it to be seen, it is commonly so near the hori- 
zon as to be lost in the vapors which are seen in that direction. 
Still, by watching for favorable moments, it can be seen sev- 
eral times in the course of the year in any part of the United 
States. The following are favorable times for seeing it after 
sunset : 

1878 April 14th, August 9th, December 9th. 

1879 March 28th, July 23d, November 21st. 

1880 March 8th, July 5th, November 1st. 







290 THE SOLAR SYSTEM. 

The corresponding times in subsequent years may be found 
by subtracting 18 days from the dates for each year; that is, 
they will occur 18 days earlier in 1881 than in 1880 ; 18 days 
earlier in 1882 than in 1881, and so on. It is not necessary 
to look on the exact days we have given, as the planet is gen- 
erally visible for fifteen or twenty days at a time. Each date 
given is about the middle of the period of visibility, which ex- 
tends a week or ten days on each side. The best time for look- 
ing is in the evening twilight, about three-quarters of an hour 
after sunset, the spring is in this respect much more favorable 
than autumn. 

Aspect of Mercury. — Mercury shines with a brilliant white 
light, brighter than that of any fixed star, except, perhaps, 
Sirius. It does not seem so bright as Sirius, because it can 
never be seen at night except very near the horizon. Owing 
to the great eccentricity of its orbit and the great variations of 
its distance from the earth, its brilliancy varies considerably ; 
but the favorable times we have indicated are near those of 
greatest brightness. 

Viewed with a telescope under favorable conditions, Mer- 
cury is seen to have phases like the moon. When beyond the 
sun, it seems round and small, being only about 5" in diame- 
ter. When seen to one side of the sun, near its greatest ap- 
parent angular distance, it appears like a half-moon. When 
nearly between the sun and earth, its diameter is between 10 " 
and 12", but only a thin crescent is visible. The manner in 
which these various phases are connected with the position of 
the planet relative to the earth and sun is the same as in the 
case of Venus, and will be shown in the next section. 

Rotation, Figure, Atmosphere, etc. — About the beginning of 
the present century Schroter, the celebrated astronomer of 
Lilienthal, who made the telescopic study of the planets a 
speciality, thought that at times, when Mercury presented the 
aspect of a crescent, the south horn of this crescent seemed 
blunted at certain intervals. He attributed this appearance to 
the shadow of a lofty mountain, and by observing the times 
of its return was led to the conclusion that the planet revolved 






TRANSITS OF MERCURY. 291 

on its axis in 24 hours 5 minutes. lie also estimated the 
height of the mountain at twelve miles. But the more power- 
ful instruments of modern times have not confirmed these 
conclusions, and they are now considered as quite doubtful, if 
not entirely void of foundation. That is, we must regard the 
time of rotation of Mercury on its axis, and, of course, the 
position of that axis, as not known with certainty, but as per- 
haps very nearly 24 hours. 

The supposed atmosphere of Mercury, the deviation of its 
body from a spherical form, and many other phenomena 
which observers have described, must be received with the 
same scepticism. No deviation from a spherical form can be 
considered as proved, the discordance of the measures showing 
that the supposed deviations are really due to errors of obser- 
vation. So, also, the appearances which many observers have 
attributed to an atmosphere are all to be regarded as optical 
illusions, or as due to the imperfections of the telescope made 
use of. From measures of its light at various phases Zollner 
has been led to the conclusion that Mercury, like our moon, 
is devoid of any atmosphere sufficiently dense to reflect the 
light of the sun. If this doubt and uncertainty seems surpris- 
ing, it must be remembered that the nearness of this planet to 
the sun renders it a very difficult object to observe with accu- 
racy. We must look at it either in the daytime, when the air 
is disturbed by the sun's rays, or in the early evening, when the 
planet is very near the horizon, and therefore in an unfavorable 
situation. 

Transits of Mercury. — Transits of this planet across the face 
of the sun are much more frequent than those of Yen us, the 
average interval between successive transits being less than ten 
years, and the longest interval thirteen years. These transits 
are always looked upon with great interest by astronomers, on 
account of the questions to which they have given rise. From 
the earliest as;es in which it was known that Mercury moved 
around the sun, it was evident that it must sometimes pass be- 
tween the earth and the sun ; but its diameter is too small to 
admit of its being seen in this position with the naked eye. 



292 THE SOLAR SYSTEM. 

The first actual observation of Mercury projected on the face 
of the sun was made by Gassendi, on November 7th, 1631. 
His mode of observation was that already described for viewing 
the solar spots, the image of the sun being thrown on a screen 
by means of a small telescope. He came near missing his ob*- 
servation, owing to his having expected that the planet would 
look much larger than it did. The imperfect telescopes of 
that time surrounded every brilliant object with a band of 
diffused light which greatly increased its apparent magni- 
tude, so that Gassendi had no idea how small the planet .really 
was. 

Gassendi's observation was hardly accurate enough to be of 
any scientific value at the present time. It was not till 1677 
that a really good observation was made. Halley, of England, 
in. that year was on the island of St. Helena, and, being pro- 
vided with superior instruments, was fortunate enough to make 
a complete observation of a transit of Mercury over the sun 
which occurred on November 7th. We have already men- 
tioned the great accuracy which he attributed to his observa- 
tion, and the phenomenon of the black drop which he was the 
first to see. 

The following are the dates at which it has been calculated 
that transits of Mercury will occur during the remainder of 
the present century. The first transit will be visible over the 
whole United States, and the second on the Pacific coast. 

1878 May 6th. 1894 November 10th. 

1881 November 7th. 1901 November 4th. 

1891 May 9th. I 

§ 2. The Supposed Intra- Mercurial Planets. 

At the present time the greatest interest which attaches to 
transits of Mercury arises from the conclusion which Lever- 
rier has drawn from a profound comparison of transits ob- 
served before 1848 with the motion of Mercury as determined 
from the theory of gravitation. This comparison indicates, 
according to Leverrier, that the perihelion of Mercury moves 
more rapidly by 40" a century than it ought to from the grav- 



THE SUPPOSED INTRA- MERCURIAL PLANETS. 293 

itation of all the known planets of the system. He accounted 
for this motion by supposing a group of small planets between 
Mercury and the sun, and the question whether such planet- 
exist, therefore, becomes important. 

Apparent support to Leverrier's theory is given by the fact 
that various observers have within the past century recorded 
the passage over the disk of the sun of dark bodies which had 
the appearance of planets, and which went over too rapidly or 
disappeared too suddenly to be spots. But when we examine 
these observations, we rind that they are not entitled to the 
slightest confidence. There is a large class of recorded as- 
tronomical phenomena which are seen only by unskilful ob- 
servers, with imperfect instruments, or under unfavorable cir- 
cumstances. The fact that they are not seen by practised ob- 
servers with good instruments is sufficient proof that there is 
something wrong about them. Now, the observations of in- 
tra-Mercurial planets belong to this class. Wolf has collected 
nineteen observations of unusual appearances on the sun, ex- 
tending from 1761 to 1S65, but, with two or three exceptions, 
the observers are almost unknown as astronomers. \\\ at least 
one of these cases the observer did not profess to have seen 
anything like a planet, but only a cloud-like appearance. On 
the other hand, for fifty years past the sun has been constant- 
ly and assiduously observed by such men as Schwabe, (Harring- 
ton, Secchi, and Spoerer, none of whom have ever recorded 
anything of the sort. That planets in such numbers should 
pass over the solar disk, and be seen by amateur observers, 
and yet escape all these skilled astronomers, is beyond all 
moral probability. 

In estimating this probability we must remember that a 
real planet appearing on the sun would be far more likely to 
be recognized by a practised than by an unpractised observer, 
much as a new species of plant or animal is more likely to be 
recognized by a naturalist than by one who is not such. One 
not accustomed to the close study of the solar spots might 
have some difficulty in distinguishing an unusually round spot 
from a planet. He is also liable to be deceived in various 



294 THE SOLAR SYSTEM. 

ways.* For instance, the sun, by his apparent diurnal motion, 
presents different parts of the edge of his disk to the hori- 
zon in the course of, a day ; he seems, in fact, in the north- 
ern hemisphere to turn round in the same direction with the 
hands of a watch. Hence, if a spot is seen near the edge, of 
his disk it will seem to be in motion, though really at rest. 
On the other hand, should an experienced observer see a planet 
projected on the sun's face, he could hardly fail to recognize it 
in a moment ; and should any possible doubt exist, it would be 
removed by a very brief scrutiny. 

The strongest argument against these appearances being 
planets is, that the transit of a planet in such a position could 
not be a rare phenomenon, but would necessarily repeat itself 
at certain intervals, depending on its distance from the sun 
and the inclination of its orbit. For instance, supposing an 
inclination of 10°, which is greater than that of any of the 
principal planets, and a distance from the sun one-half that 
of Mercury, the planet would pass over the face of the sun, 
on the average, about once a year, and its successive transits 
would occur either very near the same day of the year, or on 
a certain day of the opposite season. The supposed transits 
to which we have referred occur at all seasons, and if we sup- 
pose them real, we must suppose, as a logical consequence, 
that the transits of these several planets are repeated many 
times a year, and yet constantly elude the scrutiny of all good 
observers, though occasionally seen by unskilled ones. This is 
a sufficient reductio ad absurdum of the theory of their reality. 

It is very certain, then, that if the motion of the perihelion 
of Mercury is due to a group of planets, they are each so 
small as to be invisible in transits across the sun. They must 

* Some readers may recall Butler's sarcastic poem of the "Elephant in the 
Moon," as illustrative of the possibility of an observer being deceived by some pe- 
culiarity of his telescope. In one instance, about thirty years since, a telescopic 
observation of something which we now know must have been flights of distant 
birds over the disk of the sun was recorded, and published in one of the leading 
astronomical journals, as a wonderful transit of meteors. The publication was 
probably not seriously intended, the description being a close parallel to that of 
the satirical poet. See Astronomische Nachrichten, No. 549. 



THE PLANET VEX US. 295 

also be so small as to be invisible during total eclipses of the 
sun, because they have always failed to show themselves then. 
But to produce the observed effect on Mercury, their total 
mass must be three or four times that of Mercury. Being so 
small individually, and so large in the aggregate, their num- 
ber must be counted by thousands; and if seen at all, they 
will be seen only as a cloud-like mass. Now, in the zodiacal 
light we have such a mass, and the question arises whether the 
matter which reflects this light can be that which affects the 
motions of Mercury. Although the affirmative of this ques- 
tion involves nothing intrinsically improbable, it cannot be 
accepted without further investigation. The delicate point 
involved is, that unless we suppose the hypothetical group of 
planetoids to move nearly in the plane of the orbit of Mercury, 
they must change the node of that planet as well as its peri- 
helion. Now, the observations discussed by Leverrier do not 
show any motion of the node above that due to the action of 
the known planets. We thus reach the enforced conclusion 
that if the motion of the perihelion is due to the cause as- 
signed by Leverrier, the planetoids which cause it must, in the 
mean, move in nearly the same plane with Mercury, But it 
has not yet been shown that the axis of the zodiacal light de- 
viates from the ecliptic by so great an angle as the orbit of 
Mercury, namely 7°. A great deal of research — more, in fact, 
than is likely to be applied to the subject during the present 
generation — will be required before the question can be settled. 

§ 3. The Planet Venus. 

The planet Yen us moves around the sun about half - way 
between the orbits of Mercury and the earth, its mean distance 
from the sun being 67 millions of miles. Its orbit is more 
nearly circular than that of any of the other principal planets. 
It is very nearly the size of the earth, its diameter being little. 
if any, more than four per cent, less than that of our globe. 
Next to the sun and moon, it is the most brilliant object in 
the heavens, sometimes casting a very distinct shadow. It 
never recedes more than^about 45° from the sun, and is, there- 



296 THE SOLAR SYSTEM. 

fore, seen by night only in the western sky in the evening, or 
the eastern sky in the morning, according as it is east or west 
of the sun. There is, therefore, seldom any difficulty in rec- 
ognizing it. When at its greatest brilliancy, it can be clearly 
seen by the naked eye in the daytime, provided that one knows 
exactly where to look for it. It was known to the ancients by 
the names of Hesperus and Phosphorus, or the evening and 
the morning star, the former name being given when the 
planet, being east of the sun, was seen in the evening after 
sunset, and the latter when, being to the west of the sun, it 
was seen in the east before sunrise. It is said that before the 
birth of exact astronomy Hesperus and Phosphorus were sup- 
posed to be two different bodies, and that it was not until 
their motions were studied, and the one was seen to emerge 
from the sun's rays soon after the other was lost in them, that 
their identity was established. 

Aspect of Venus. — To the unaided eye Venus presents the 
appearance of a mere star, distinguishable from other stars 
only by its intense brilliancy. But when Galileo examined 
this planet with his telescope, he found it to exhibit phases 
like those of the moon. Desiring to take time to assure him- 
self of the reality of his discovery, without danger of losing 
his claim to priority through some one else in the mean time 
making it independently, he published the following anagram, 
in which it was concealed : 

" Hsec immatura a me jam frustra leguntur o. y." 
(These unripe things are now vainly gathered by me). 

By transposing the letters of this sentence he afterwards 
showed that they could be made into the sentence, 

"Cynthise figuras remnlatur mater amornm " 
(The mother of the loves imitates the phases of Cynthia). 

That the disk of Venus was not round was first noticed by 
Galileo in September, 1610. A computation of its position 
at that time shows that it must have been a little gibbous, 
more than half of its face being illuminated; but after a 



THE PLANET VENUS. 297 

few months it changed into a crescent. Therefore Galileo 

could not have found it necessary to wait long before explain- 
ing his anagram. 

The variations of the aspect and apparent magnitude of 
Venus are very great. When beyoud the sun, it is at a dis- 
tance of 160 millions of miles, and presents the appearance 
of a small round disk 10" in diameter. When nearest the 
earth, it is only 25 millions of miles distant ; and if its whole 
face were visible, it would be more than 60" in diameter. 




c 

* • # 

Feq. T4 Phases of Venae, showing apparent figure and magnitude of the bright and dark 

portions of the planet in various points of its orbit. 

But, being then on the same side of the sun with us, its dark 
hemisphere is turned towards us, except, perhaps, an extreme- 
ly thin crescent of the illuminated hemisphere. Between 
these two positions it goes through all the intermediate 
phases, the universal rule of which is that the nearer it is 
to the earth, the smaller the proportion of its apparent disk 
which is illuminated ; but the larger that disk would appear 
could the whole of it be seen. Its greatest brilliancy occurs 
between the time of its greatest elongation from the sun and 
its inferior conjunction. 

Supposed Eolation of Venus. — The earlier telescopists natu- 
rally scrutinized the planets very carefully, with a view of find- 
ing whether there were any inequalities or markings on their 
surfaces from which the time of rotation on their axes could 
he determined. In April, 1667, Cassini saw, or thought he 
saw, a bright spot on Venus, by tracing which for several suc- 
cessive evenings he found that the planet revolved in between 
23 and 24 hours. Sixty years later Blanchini, an Italian as- 



298 THE SOLAR SYSTEM. 

tronomer, whose telescope is shown on page 112, supposed that 
he found seven spots on the planet, which he considered to be 
seas. By watching, them from night to night, he concluded 
that it required more than 24 days for Venus to revolve on 
its axis. This extraordinary result was criticised by the sec- 
ond Cassini, who showed that Blanchini, only seeing the plan- 
et a short time each evening, and finding the spots night after 
night in nearly the same position, concluded that it had moved 
very little from night to night ; whereas, in fact, it had made 
a complete revolution, and a little more. At the end of 24 
days it would be seen in its original position, but would have 
made 25 revolutions in the mean time, instead of one only, as 
Blanchini supposed. This would make the time of rotation 
23 hours 2|- minutes, while Cassini found 23 hours 15 minutes 
from his father's observations. 

Between 1788 and 1793- Schroter applied to Venus a mode 
of observation similar to that he used to find the rotation of 
Mercury. Watching the sharp horns when the planet appear- 
ed as a crescent, he thought that one of them was blunted at 
certain intervals. Attributing this appearance to a high moun- 
tain, as in the case of Mercury, he found a time of rotation 
of 23 hours 21 minutes. 

On the other hand, Herschel was never able to see any per- 
manent markings on Venus. He thought he saw occasional 
spots, but they varied so much and disappeared so rapidly that 
he could not gather any evidence of the rotation of the plan- 
et. He therefore supposed that Venus was surrounded by an 
atmosphere, and that whatever markings might be occasional- 
ly seen were due to clouds or other varying atmospheric phe- 
nomena. 

In 1842, De Vico, of Rome, came to the rescue of the older 
astronomers by publishing a series of observations tending to 
show that he had rediscovered the markings found by Blan- 
chini more than a century before. He deduced for the time 
of rotation of the planet 23 hours 21 minutes 22 seconds. 

The best-informed astronomers of the present day look with 
suspicion on nearly all these observations, being disposed to 



THE PLANET VENUS. 299 

sustain the view of Ilerschel, though on grounds entirely dif- 
ferent from those on which he founded it. It is certain that 
there are plenty of observers of the present day, with instru- 
ments much better than those of their predecessors, who have 
never been able to see any permanent spots. The close agree- 
ment between the times of rotation found by the older ob- 
servers is indeed striking, and might seem to render it certain 
that they must have seen spots which lasted several days. It 
must also be admitted in favor of these observers that a fine 
steady atmosphere is as necessary for such observations as a 
fine telescope, and it is possible that in this respect the Italian 
astronomers may be better situated than those farther north. 
But the circumstance that the deduced times of rotation in 
the cases both of Mercury and Venus differ so little from that 
of the earth is somewhat suspicious, because if the appearance 
were due to any optical illusion, or imperfection of the tele- 
scope, it might repeat itself several days in succession, and 
thus give rise to the belief that the time of rotation was near- 
ly one day. The case is one on which it is not at present pos- 
sible to pronounce an authoritative decision ; but the balance 
of probabilities is largely in favor of the view that the rota- 
tation of Venus on its axis has never been seen or determined 
by any of the astronomers who have made this planet an ob- 
ject of study.* 

Atmosphere of Venus. — The appearance of Venus when near- 
ly between us and the sun affords very strong evidence of the 
existence of an atmosphere. The limb of the planet farthest 
from the sun is then seen to be illuminated, so that it appears 
as a complete circle of light! If only half the globe of the 
planet were illuminated by the sun, this appearance could 
never present itself, as it is impossible for an observer to see 
more than half of a large sphere at one view. There is no 

* The latest physical observations on Venus with which I am acquainted are 
those of Dr. Vogel at Bothkamp, in Part II. of the " Bothkamp Observations" 
(Leipzig, Engelmann, 1873). The result to which these observations point is that 
the atmosphere of Venus is filled with clouds so dense that the solid body of the 
planet can not be seen, and no time of rotation can be determined. 



300 THE SOLAR SYSTEM. 

known way in which the sun can illuminate so much more 
than the half of Venus as to permit a complete circle of light 
to be seen except by the refraction of an atmosphere. 

The appearance to which w T e allude was first noticed by 
David Rittenhouse, of Philadelphia, while observing the tran- 
sit of Venus on June 3d, 1769. When Venus had entered 
about half-way upon the sun's disk, so as to cut out a notch of 
the form of a half-circle, that part of the edge of the planet 
which was off the disk appeared illuminated so that the out- 
line of the entire planet could be seen. As this appearance 
was not confirmed by other observers, it seems to have excit- 
ed no attention. But it was found by Madler in 1849 that 
when Venus was near inferior conjunction, the visible crescent 
extended through more than a half-circle. This showed that 
more than half the globe of Venus was illuminated by the 
sun, and Madler, computing the refractive power of the atmos- 
phere which would be necessary to produce this effect, found 
that it would exceed that of our own atmosphere ; the hori- 
zontal refraction being 44', w T hereas on the earth it is only 
34'. He therefore concluded that Venus was surrounded by 
an atmosphere a little more dense than that of the earth. 

The next important observation of the kind was made by 
Professor C. S. Lyman, of Yale College. In December, 1866, 
Venus was very near her node at inferior conjunction, and 
passed unusually near the line drawn from the earth to the 
sun. Examining the minute crescent of the planet with a 
moderate-sized telescope, he found that he could see the entire 
circle of the planet's disk, an exceedingly thin thread of light 
being stretched round the side farthest from the sun. So far 
as known, this was the first time that the whole circle of Venus 
had been seen in this way since the time of Rittenhouse. It 
is remarkable that both observations should have been made 
by isolated observers in America. 

Notwithstanding the concurrent testimony of Rittenhouse, 
Madler, and Lyman, the bearing of their observations on what 
was to be expected during the transit of Venus in December, 
1874, was entirely overlooked. Accordingly, many of the ob- 



The i'lanet venub. 301 

servers were quite taken by surprise to find that when Venus 
was partly on and partly off the sun, the outline of that part 
of her disk outside the sun could be distinguished by a deli- 
cate line of light extending around it. In some cases the 
time of internal contact at egress of the planet was missed, 
through the observer mistaking this line of light for the limb 
of the sun. 

That no one but Rittenhouse saw this line of light during 
the transit of 1769 is to be attributed to the low altitude of 
the planet at most of the stations, and to the imperfect char- 
acter of many of the instruments used. It is also to be re- 
marked that the observers of that time had an erroneous no- 
tion of the appearance which would be presented by an atmos- 
phere of Venus. It was supposed that the atmosphere would 
give the planet a nebulous border when on the sun, caused by 
the partial absorption of the light in passing through it. Cap- 
tain Cook, at Otaheite, made separate observations of the 
contacts of the supposed atmosphere and of the planet with 
the limb of the sun. In fact, however, it would not lie possi- 
ble to see any indications of an atmosphere under such cir- 
cumstances, for the reason that the light passing through its 
denser portions would be refracted entirely out of its course, 
so as not to reach an observer on the earth at all. 

The spectroscope shows no indication that the atmosphere 
of Venus exerts any considerable selective absorption upon 
the light which passes through it. No new and well-marked 
spectral lines are found in the light reflected from the planet, 
nor has the spectrum been certainly found to differ from the 
regular solar spectrum, except, perhaps, that some of the lines 
are a little stronger. This would indicate that the atmosphere 
in question does not differ in any remarkable degree from our 
own, or, at least, does not contain gases which exert a power- 
ful selective absorption on light. 

Supposed Visibility of the Dark Hemisphere of Venus. — Manv 
astronomers of high repute have seen the dark atmosphere of 
Venus slightly illuminated, the planet presenting the appear- 
ance known as " the old moon in the new moon's arms," which 



302 THE SOLAR SYSTEM. . 

may be seen on any clear evening three or four days after the 
change of the moon. It is well known that in the case of 
the moon her dark hemisphere is thus rendered visible by the 
lio-ht reflected from the earth. But in the case of Venus, 
there is no earth or other body large enough to shed so much 
light on the dark hemisphere as to make it visible. There 
being no sufficient external source of light, it has been attrib- 
uted to a phosphorescence of the surface of the planet. If 
the phosphorescence were always visible under favorable cir- 
cumstances, there would be no serious difficulty in accepting 
this explanation. But, being only rarely seen, it is hard to 
conceive how an y merely occasional cause could act all at 
once over the surface of a planet the size of our globe, so as 
to make it shine. Indeed, one circumstance makes it ex- 
tremely difficult to avoid the conclusion that the whole ap- 
pearance is due to some unexplained optical illusion. The 
appearance is nearly always seen in the daytime or during 
bright twilight — rarely or never after dark. But such an il- 
lumination would be far more easily seen by night than by 
day, because during the day an appearance easily seen at 
night might be effaced by the light of the sky. If, then, the 
phenomenon is real, why is it not seen when the circumstances 
are such that it should be most conspicuously visible? This 
is a question to which no satisfactory answer has been given, 
and until it is answered we are justified in considering the ap- 
pearance to be purely optical. 

Supposed Satellite of Venus. — No better illustration of the er- 
rors to which observations with imperfect instruments are lia- 
ble can be given than the supposed observations of a satellite 
of Venus, made when the telescope was still in its infancy. 
In 1672, and again in 1686, Cassini saw a faint object near 
Venus which exhibited a phase similar to that of the planet. 
But he never saw it except on these two occasions. A similar 
object was reported by Short, of England, as seen by him on 
October 23d, 1740. The diameter of the object was a third 
of that of Venus, and it exhibited a similar phase. Several 
other observers saw the same thing between 1760 and 1764. 



THE PLANET VENUS, 303 

One astronomer went so far as to compute an orbit from all 
the observations ; but it was an orbit in which no satellite of 
Yen us could possibly revolve unless the mass of the planet were 
ten times as great as it really is. A century has now elapsed 
without the satellite having been seen, and the fact that dur- 
ing this century the planet has been scrutinized with better 
telescopes than any which were used in the observations re- 
ferred to affords abundant proof that the object was entirely 
mythical. 

How the observers who thought they saw the object could 
have been so deceived it is impossible, at this distance of 
time, to say with certainty. Had they been inexperienced, 
we could say with some confidence that they were misled by 
the false images produced to some extent in every telescope 
by the light reflected from the cornea of the eye against the 
nearest surface of the eye-piece, and thence back again into 
the eye. Similar images are sometimes produced by the re- 
flection of light between the surfaces of the various lenses of 
the eye - piece. They are well known to astronomers under 
the name of " ghosts ;" and one of the first things a young ob- 
server must learn is to distinguish them from real objects. 
They may also arise from a slight maladjustment of the lenses 
of the eye-piece, and if, proceeding from this cause, they are 
produced only when the actual object is in the centre of the 
field, they may, for the moment, deceive the most experienced 
observer.* If, in an ordinary achromatic telescope, in which 
the interior curvatures of the lenses are the same, the latter 
are not exactly at the same distance all the way round, a ghost 
will be seen along-side of every bright object in all positions. 
It is probable that all the observations alluded to were the re- 
sults of some sort of derangements in the telescope, producing 
false images by reflection from the glasses. 

* One of the eye-pieces of the great "Washington telescope shows a beautiful 
little satellite along -side the planet Uranus or Neptune when the image of the 
planet is brought exactly in the centre of the field of view, but it disappears as 
soon as the telescope is moved. The writer was deceived by this appearance on 
two occasions while scrutinizing these planets for close satellites. 

21 



304 THE SOLAE SYSTEM. 

§ 4. The Earth. 

Our earth is the third planet in the order of distance from 
the sun, and slightly the largest of the inner group of four. 
Its mean distance from the sun is about 92J millions of miles ; 
but it is a million and a half less than this mean on January 
1st of every year, and as much greater on July 1st. That 
is, its actual distance varies from 91 to 94 millions of miles. 
As already remarked, these numbers are uncertain by several 
hundred thousand miles. 

Much of what we may call the astronomy of the earth — 
such as its figure and mass, the length of the year, the obliq- 
uity of the ecliptic, the causes of the changes in the seasons 
and in the length of the days — has already been treated in 
the chapter on gravitation, so that we have little of a purely 
astronomical character to add here. The features of its sur- 
face and the phenomena of its atmosphere belong rather to 
geography and meteorology than to astronomy. But its consti- 
tution gives rise to several questions in the treatment of which 
astronomical considerations come into play. Prominent among 
these is that of the state of the great interior mass of our 
globe, whether solid or liquid. It is well known that wher- 
ever we descend into the solid portions of the, earth, we find a 
rise in temperature, going on uniformly with the depth, at a 
rate which nowhere differs greatly from 1° Fahrenheit in 50 
feet. This rise of temperature has no connection with the 
sea-level, but is found at all points of the surface, no matter 
how elevated they may be. Wherever a difference of temper- 
ature like this exists, there is necessarily a constant transfer of 
heat from the warmer to the cooler strata by conduction. In 
this way, the inequality would soon disappear by the warmer 
strata cooling off, if there were not a constant supply of heat 
inside the earth. The rise of temperature, therefore, cannot 
be something merely superficial, but must continue to a great 
depth. If we trace to past times the conditions which must 
have existed in order that the increase might show itself at the 
present time, we shall find it almost certain that, a thousand 



THE EARTH. 305 

years ago, the whole earth was red-hot at a distance of ten or 
fifteen miles below its surface; because otherwise its interior 
could not have furnished the supply of heat which now ca 
the observed increase. This being the case, it is probably red- 
hot still, since it would be absurd to expect a state of tilings 
like this to be merely temporary. In a word, we have every 
reason to believe that the increase of say 100° a mile contin- 
ues many miles into the interior of the earth. Then we shall 
have a red heat at a distance of 12 miles, while, at the 
depth of 100 miles, the temperature will be so high as t<» 
melt most of the materials which form the solid crust of the 
globe. 

We are thus led to the theory, very generally received by 
geologists, that the earth is really a sphere of molten matter 
surrounded by a comparatively thin solid crust, on which we 
live. This crust floats, as it were, on the molten interior. It 
must be confessed that geological facts are, on the whole, fa- 
vorable to this view. Observations on the pendulum have 
been supposed to show that the specific 
gravity of the earth under the great 
mountain chains is generally less than in 
the adjoining plains, which is exactly the 
result that would flow from the theory. 
The heavier masses, pressing upon the in- 
terior fluid, would tend to elevate the sur- 
rounding lighter masses, and when the two Fig. 75. —Showing thickness 
were in equilibrium, the latter would be f lh t e e * rth ' s c . rus . t ■£** 

1 ' > mg to the geological theo- 

the higher, as a floating block of pine ry of a molten interior. 

j mi 1 . -i r .1 , The circle is thicker in 

wood will rise higher out of the water proportion than the solid 
than a block of oak. Boiling springs in crust - 
many parts of the globe show that there are numerous hot re- 
gions in the earth's interior, and this heat cannot be merely 
local, because then it would soon be dissipated. But the geol- 
ogist finds the strongest proof of the theory in volcanoes and 
earthquakes. The torrents of lava which have been thrown 
out of the former through thousands of years show that there 
are great volumes of molten matter in the earth's interior, 




306 THE SOLAR SYSTEM. 

while the latter show this interior to be subject to violent 
changes which a solid could not exhibit. 

But mathematicians have never been able entirely to rec- 
oncile the theory in question with the observed phenomena of 
precession, nutation, and tides. To all appearance, the earth 
resists the tide-producing action of the sun and moon exactly 
as if it were solid from centre to circumference. Sir William 
Thomson has shown that if the earth were less rigid than steel, 
it would yield so much to this action that the tides would be 
much smaller than on a perfectly rigid earth ; that is, the at- 
traction of the bodies in question would draw the earth itself 
out into an ellipsoidal form, instead of drawing merely the 
waters of the ocean. Earth and ocean moving together, we 
could see no tides at all. If the earth were only a thin shell 
floating on a liquid interior, the tides would be produced in 
the latter ; the thin shell would bend in such a way that the 
tides in the ocean would be nearly neutralized. Again, the 
question has arisen whether the liquid interior would be af- 
fected by precession ; whether, in fact, the crust would not slip 
over it, so that in time the liquid would rotate in one direc- 
tion, and the crust in another. Altogether, the doctrine of the 
earth's fluidity is so fraught with difficulty that, notwithstand- 
ing the seeming strength of the evidence in its favor, it must 
be regarded as at least very doubtful. It may be added that 
no one denies that the interior of our planet is intensely hot — 
hot enough, in fact, to melt the rocks at its surface — but it 
is supposed that the enormous pressure of the outer portions 
tends to keep the inner part from melting. Nor is it ques- 
tioned by Sir William Thomson that there are great volumes 
of melted matter in the earth's interior from which volcanoes 
are fed; but he maintains that, after all, these volumes are 
small compared with that of the whole earth. 

Refraction of the Atmosphere. — If a ray of light pass through 
our atmosphere in any other than a vertical direction, it is 
constantly curved downwards by the refractive power of that 
medium. The more nearly horizontal the course of the ray, 
the greater the curvature. In consequence of this, all the 



THE EARTH. 3" 7 

heavenly bodies appear a little nearer the zenith, or a little 
higher above the horizon, than they actually are. The dis- 
placement is too small to be seen by the naked eye except 
quite near the horizon, where it increases rapidly, amounting 
to more than half a degree at the horizon itself. Consequent- 
ly, at any point where we have a clear horizon, as on a prairie. 
or the sea-shore, the wiiole disk of the sun will be seen above 
the horizon when the true direction is below it. A slight in- 
crease is thus given to the length of the day. The sun in our 
latitudes always rises three or four minutes sooner, and - 
three or four minutes later, than he would if there were no 
atmosphere. At the time of the equinoxes, if we suppose the 
day to begin and end when the centre of the sun is on the 
horizon, it is not of the same length with the night, but is six 
or eight minutes longer. If we suppose the day to begin with 
the rising of the sun's upper limb, and not to end till the same 
limb has set, then we must add some three minutes more t<> 
its length. 

If, standing on a hill, we watch the sun rise or set over the 
ocean, one effect of refraction will be quite clearly visible. 
When his lower limb almost seems to touch the water, it will 
be seen that the form of his disk is no longer round, but ellip- 
tical, the horizontal diameter being greater than the vertical. 
The reason of this is that the lower limb is more elevated by 
refraction than the upper one, and thus the vertical diameter 
is diminished. 

In practical astronomy, all observations of the altitude of 
the heavenly bodies above the horizon must be corrected for 
refraction, the true altitude being always less than that ob- 
served. Very near the zenith the refraction is about 1" for 
every degree, or xgW P art the distance from the zenith. But 
it increases at first in the proportion of the tangent of the ze- 
nith distance, so that at 45°, or half-way between the zenith 
and the horizon, it amounts to 60"; at the horizon it is 34'. 

The Aurora Borealis. — This phenomenon, though so well 
known, is one of which great difficulty has been found in giv- 
ing a satisfactory explanation. That it is in some way con- 



308 



THE SOLAR SYSTEM. 




Fig. 76.— Distribution of auroras, after Loomis. The darker the color, the more frequently 

auroras are seen. 

nected with the pole of the earth is shown by the fact that 
its frequency depends on the latitude. In the equatorial re- 
gions of our globe it is quite rare, and increases in frequency 
as we go north. But the region of greatest frequency seems 



THE EARTH. 



309 



to be, not the poles, but the neighborhood of the Arctic Cir- 
cle, from which it diminishes towards both the north and the 
south. This is shown more exactly in Professor Loomis's 
auroral map, of which we give a copy on the preceding page. 
A close study of the aurora indicates that its connection is 
not with the geographical, but with the magnetic pole. Two 
distinct kinds of light are seen in the aurora ; or we might 
say that the light assumes two distinct forms, of which some- 
times the one and sometimes the other preponderates. They 
are as follows : 

1. The cloud-like form. This consists of a large irregular 
patch of light, frequently of a red or purple tinge. It is seen 
in every direction, but more frequently in or near the northern 
horizon, where it assumes the form of an arch or crown of 
light. The two ends of the arch rest on the horizon, one on 
each side of the north point. The middle of the arch rises a 
few degrees above the horizon. 




Fig. 77.— View of aurora 



2. The streamer or pillar form. This form consists of long 
streamers or pillars, which extend in the direction of the dip- 
ping magnetic needle. They look curved or arched, like the 
celestial sphere on which they are projected, but they are re- 
ally straight. They are in a state of constant motion. Some- 



310 THE SOLAR SYSTEM. 

times they are spread out in the form of an immense flag 
with numerous folds, dancing, quivering, and undulating, as 
if moved by the wind. 

Electric Nature of the Aurora. — There is abundant evidence 
that the aurora is intimately connected with the electricity 
and magnetism of the •earth. During a brilliant aurora such 
strong and irregular currents of electricity pass through the 
telegraph wires that it is difficult to send a despatch. Some- 
times the current runs with such force that a message may 
be sent without a battery. The magnetic needle is also in a 
state of great agitation. Before the spectroscope came into 
use, these electric phenomena gave rise to the opinion that 
the aurora was due entirely to currents of electricity passing 
through the upper regions of the atmosphere from one pole to 
the other. But recent researches seem to show that, though 
this view may be partly true, it is far from the whole truth, 
and does not afford a complete explanation. The great height 
of the aurora and the nature of its spectrum both militate 
against it. 

Height of the Aurora. — Several attempts have been made in 
recent times to determine the height of the aurora above the 
surface of the earth, by simultaneous observations of some 
prominent streamer or patch of light from several far-distant 
stations. The general result is that it extends to the height of 
from 400 to 600 miles. But the evidence of shooting- stars 
and meteors seems to indicate that the limit of the atmosphere 
is between 100 and 110 miles in height. If it extends above 
this, it must be too rare to conduct electricity long before it 
reaches the greatest height of the aurora ; indeed, it is doubt- 
ful whether it does not attain this rarity at a height of 40 or 
50 miles. If, then, the aurora really extends to the great 
height we have mentioned, and still exists in a gaseous medi- 
um, it seems difficult to avoid the conclusion that this medium 
is something far more ethereal than the gases which form our 
atmosphere. It would, however, be unphilosophical to assume 
the existence of such a medium without some other evidence 
in its favor than that afforded by the aurora. We must in- 



THE EARTH. 



11 



elude the aurora among those things in which modern ob- 
servations have opened up more difficulties than modern theo- 
ries have explained. 

Spectrum of the Aurora. — The spectrum of the aurora is so 
far from uniform as to be quite puzzling. There is one char- 
acteristic bright line in the green part of the spectrum, known 
as Angstrom's line, from its first discoverer. This was the 
only line Angstrom could see: he therefore pronounced the 
light of the aurora to be entirely of one color. Subsequent 
observers, however, saw many additional lines, but they were 
different in different auroras. Among those who have made 
careful studies of the aurora with the spectroscope are the 
late Professor Winlock, of Harvard University; Professor 
Barker, of Philadelphia ; and Dr. H. C. Vogel, formerly of 
Bothkamp. 




D Eft F 

Fig. 78 Spectrum of two of the great auroras of 1871, after Dr. H. C. VogeL 

Fig. 78 shows the spectra of two auroras, as drawn by Dr. 
Yogel. It will be seen that there is one fine bright line be- 
tween D and F, which would fall in the yellowish-green part 
of the spectrum, while the others are all broad, ill -defined 
bands. Dr. Yogel notices a remarkable connection between 
these lines and several groups of lines produced by the vapor 
of iron, and inquires whether this vapor can possibly exist in 
the upper regions of our atmosphere. A more complete study 
of the spectra of vapors at different pressures and tempera- 
tures is necessary before we can form a decided opinion as to 
what the aurora really is. i 






THE SOLAR SYSTEM. 



Of the supposed periodicity of the aurora, and its connection 
with sun-spots, we have already spoken. Granting the reality 
of this connection, 'we may expect that auroras will be very 
frequent between the years 1880 and 1884; and if this ex- 
pectation is realized, little doubt of the connection will remain. 

§ 5. The Moon. 

The moon is much the nearest to us of all the heavenly 
bodies ; no other, except possibly a comet, ever coming nearer 
than a hundred times her distance. Her mean distance is, in 
round numbers, 240,000 miles. Owing to the ellipticity of her 
orbit and the attractive force of the sun, it varies from ten to 
twenty thousand miles on each side of this mean in the course 
of each monthly revolution. The least possible distance is 
221,000 miles ; the greatest is 259,600 miles. It very rarely 
approaches either of these limits, the usual oscillation being 
about 13,000 miles on each side of the mean distance of 
240,300. The diameter of the moon is 2160 miles, or some- 
what less than two-sevenths that of the earth. Her volume is 
about one-fiftieth that of the earth, and if she were as dense 
as the latter, her mass would be in the same proportion. 




Fig. 79.— Relative size of earth and moon. 



But her actual mass is only about one-eightieth that of the 
earth, showing that her density, or the specific gravity of the 
material of which she is composed, is little more than half that 



THE MOON. 313 

of our globe. Her weight is, in fact, about 3J times that of 
her bulk of water. 

The most remarkable feature of the motion of the moon is, 
that she makes one revolution on her axis in the same time 
that she revolves around the earth, and so always presents the 
same face to us. In consequence, the other side of the moon 
must remain forever invisible to human eye^. The reason of 
this peculiarity is to be found in the ellipticity of her globe. 
That she should originally have been set in revolution on her 
axis with precisely the same velocity with which she revolved 
around the earth, so that not the slightest variation in the re- 
lation of the two motions should ever occur in the course of 
ages, is highly improbable. If such had been the state of 
things, the correspondence of the two motions could not have 
been kept up without her axial rotation varying ; because, 
owing to the secular acceleration already described, the moon, 
in the course of ages, varies her time of revolution, and so 
the two motions would cease to correspond. But the effect of 
the attraction of the earth upon the slightly elongated lunar 
i^lobe is such that if the two motions are, in the beginning, 
very near together, not only will the axial rotation accommo- 
date itself to the orbital revolution around the earth, but as 
the latter varies, the former will vary with it, and thus the 
correspondence will be kept up. 

Figure, Rotation, and Libration of the Moon. — Supposing the 
shape of the moon to be the same as if it were a fluid mass, 
or covered by an ocean, it will be an ellipsoid with three un- 
equal axes. The shortest axis will be that around which it 
revolves, which is not very far from being perpendicular to 
the ecliptic. The next longest is that which lies in the direc- 
tion in which the moon moves ; while the longest of all is 
that which points towards the earth. The reason that the 
polar axis is the shortest is the same which makes the polar 
axis of the earth the shortest, that is, the centrifugal force 
generated by the revolution round that axis. If we consid- 
ered only the action of this force, we should conclude that the 
moon, like the earth, was an oblate spheroid, the equator be- 



314 THE SOLAR SYSTEM. 

ing a perfect circle. But the attraction of the earth upon the 
moon tends to elongate it in the direction of the line joining 
the two bodies, in the same way that the attraction of the moon 
upon the earth generates a tide-producing force which we have 
already explained. At the centre of the moon the attraction 
of the earth and the centrifugal force of the moon in its or- 
bit exactly balance each other. But if w r e go to the farther 
side of the moon, the centrifugal force will be greater, owing 
to the larger orbit which that part of the moon has to de- 
scribe, while the attraction of the earth will be less owing to 
the greater distance of the particles it attracts. Hence, that 
part of the moon tends to fly off from the centre and from the 
earth. On this side of the moon the case is reversed, the at- 
tractive force of the earth exceeding the centrifugal force of 
those parts of the moon, whence those parts are impelled by a 
force tending to draw them to the earth. The effect would 
be much the same as if a rope were fastened to this side of 
the moon, and constantly pulled towards the earth, while an- 
other were fastened to the opposite side, and as constantly 
pulled from the earth. Supposing the moon to be a liquid, 
so as to yield freely, it is clear that the effect of these forces 
would be to elongate her in the direction of the earth. 

The deviations from a spherical form produced by these 
causes are very minute. Taking the results of Lagrange and 
Newton, the mean axis would be 46^ feet longer than the 
shortest one, and the longest 186 feet longer than the mean 
one, or 232i feet longer than the shortest one.* These differ- 
ences are so much smaller than the average height of the 
lunar mountains that the irregularities produced by the latter 
might entirely overpower them ; but the correspondence be- 
tween the motions of rotation and revolution of the moon 
shows that there must be, on the average, a real elongation in 

* These numbers are, perhaps, not strictly correct. The extension of 186 feet 
was deduced by Newton from a comparison of the distorting powers of the centrif- 
ugal force of the earth with that of the force we have just described. He seems 
to have overlooked the fact that the small density of the moon will cause the 
elongation to be greater. 



THE MOON. 315 

the direction of the earth. This correspondence is kept up by 
the slight additional attraction of the earth upon this extension 
of the moon towards the earth, combined with the additional 
centrifugal force of the extension on the other side. Although 
these forces are not by any means the same as the distorting 
forces already described, they may be represented in the same 
way by two ropes, one of which pulls the protuberance on this 
side towards the earth, while the other pulls the protuberance 
on the other side from it. If the two protuberances do not 
point exactly towards the earth, the effect of these two minute 
forces will be to draw them very slowly into line. Conse- 
quently, notwithstanding the slow variations to which the mo- 
tion of the moon around the earth is subject in the course 
of ages, the attraction of the earth will always keep this pro- 
tuberant face turned towards us. Human eyes will never be- 
hold the other side of the moon, unless some external force 
acts upon her so as to overcome the slight balancing force 
just described, and set her in more or less rapid motion on 
her axis. If it is disappointing to reflect that we are for- 
ever deprived of the view of the other side of our satellite, we 
may console ourselves with the reflection that there is not the 
slightest reason to believe that it differs in any respect from 
this side. The atmosphere with which it has been covered, 
and the inhabitants with which it has been peopled, are no 
better than the products of a poetic imagination. 

The forces we have just described as tending to keep the 
same face of the moon pointed towards us would not produce 
this effect unless the adjustment of the two motions — that 
around the earth, and that on her axis — were almost perfect 
in the beginning. If her axial rotation were accelerated by so 
small an amount as one revolution in two or three years, there 
is every reason to believe that she would keep on revolving at 
the new rate, notwithstanding the force in question. The case 
is much like that of a very easy-turning fly-wheel, which is 
slightly weighted on one side. If we give the wheel a gentle 
/ motion in one direction or another, the weight will cause the 
wheel to turn till the heavy side is the lowest, and the wheel 



316 THE SOLAR SYSTEM. 

will then vibrate very slowly on one side and the other of this 
point. But if we give the wheel a motion rapid enough to 
carry its heavy side' over the highest point, then the weight 
will accelerate the wheel while it is falling as much as it will 
retard it while rising ; and if there were no friction, the wheel 
would keep on turning indefinitely. The question now arises, 
How does it happen that these two motions are so exactly ad- 
justed to each other that not only is the longer axis of the 
moon pointed exactly towards the earth, but not the slightest 
swing on one side or the other can be detected ? That this 
adjustment should be a mere matter of chance, without any 
physical cause to produce it, is almost infinitely improbable, 
while to suppose it to result from the mere arbitrary will of 
the Creator is contrary to all scientific philosophy. But if the 
moon were once in a partially fluid state, and rotated on her 
axis in a period different from her present one, then the enor- 
mous tides produced by the attraction of the earth, combined 
with the centrifugal force, would be accompanied by a fric- 
tion wliich would gradually retard the rate of rotation, until 
it was reduced to the point of exact coincidence with the rate 
of revolution round the earth, as we now find it. We there- 
fore see in the present state of things a certain amount of 
probable evidence that the moon was once in a state of par- 
tial fluidity. 

The force we have just described as drawing the protuber- 
ant portion of the moon towards the earth is so excessively 
minute that it takes it a long time to produce any sensible ef- 
fect ; consequently, although the moon moves more rapidly in 
some points of her orbit than in others, the force in question 
produces no corresponding change in the moon's rotation. 
The protuberance does not, therefore, always point exactly at 
the earth, but sometimes a little one side, and sometimes a lit- 
tle the other, according as the moon is ahead of or behind her 
mean place in the orbit. The result is, that the face which 
the moon presents to us is not always exactly the same, there 
being a slight apparent (not real) oscillation, due to the real 
inequality in her orbital motion. This apparent swaying is 



THE MOON. 317 

called libralion, and in consequence of it there is nearly 
tenths of the lunar surface which may, at one time or a 'other, 
come into view from the earth. 

The Lunar Day. — In consequence of the peculiarity in the 
moon's rotation which we have described, the lunar day is \ 
times as long as the terrestrial day. Near the moon's equator 
the sun shines without intermission nearly fifteen of our day-, 
and is absent for the same length of time. In consequence, 
the vicissitudes of temperature to which the surface is exposed 
must be very great. During the long lunar night the temper- 
ature of a body on the moon's surface would probably fall 
below any degree of cold that we ever experience on the earth, 
while during. the day it must become hotter than anywhere 
on our globe. 

Astronomical phenomena, to an observer on the moon, would 
exhibit some peculiarities. The earth would be an immense 
moon, going through the same phases that the moon doe* 
us; but instead of rising and setting, it would only oscillate 
back and forth through a few degrees. On the other side of 
the moon it would never be seen at all The diurnal motion 
of the stars would take place in twenty- seven of our days, 
much as they do here every day, while, as we have said, the 
sun would rise and set in 29£ of our days. 

Geography of the Moon. — With the naked eye it is quire 
readily seen that the brilliancy of the moon is far from uni- 
form, her disk being variegated with irregular dark patches, 
which have been supposed to bear a rude resemblance to a 
human face. It is said to have been a fancy of some of the 
ancient philosophers that the light and dark portions were 
caused by the reflection of the seas and continents of the ter- 
restrial globe, though it is hard to conceive of such an opin- 
ion being seriously entertained. The first rude idea of the 
real nature of the lunar surface was gained by Galileo with 
his telescope. He saw that the brighter portions of the disk 
were broken up with inequalities of the nature of mountains 
and craters, while the dark parts were, for the most part, 
smooth and uniform. Here he saw a striking resemblance to 



31 S THE SOLAR SYSTEM. 

the geographical features of our globe, and is said to have sug- 
gested that the brighter and rougher portions might be conti- 
nents, and the darl^:, smooth portions oceans. This view of the 
resemblance to terrestrial scenery is commemorated in Mil- 
ton's description of Satan's shield : 

" Like the moon, whose orb 
Through optic glass the Tuscan artist views 
At evening, from the top of Fesole, 
Or in Valdarno, to descry new lands, 
Rivers, or mountains in her spotty globe." 

i 

The opinion that the dark portions of the lunar disk were 
seas was shared by Kepler, Hevelius, and Ricciolns. The last 
two made maps of the moon in which they gave names to the 
supposed seas, which names the regions still bear, though they 
are strikingly fanciful. Among them are Oceanus Procella- 
rum (the Ocean of Storms), Mare Tranquillitatis (Sea of Tran- 
quillity), Mare Imbrium (Rainy Sea), etc. The names of great 
philosophers and astronomers were given to prominent feat- 
ures, craters, etc. 

If this resemblance between the earth and moon had been 
established ; if it had been found that our satellite really had 
seas and atmosphere, and was fitted for the support of or- 
ganic life ; still more, if any evidence of the existence of in- 
telligent beings had been found, our interest in lunar geogra- 
phy would have been immensely heightened. But the more 
the telescope was improved, the more clearly it was seen that 
there was no similarity between lunar and terrestrial scenery. 
A very slight increase of telescopic power showed that there 
was no more real smoothness in the regions of the supposed 
seas than elsewhere. The inequalities were smaller and hard- 
er to see on account of the darkness of color ; but that was 
all. The sun would have been brilliantly imaged back from 
the surfaces of the oceans in certain positions of the moon ; 
but nothing of the kind was ever seen. The polariscope 
showed that the sun's rays did not pass through any liquid at 
the moon's surface. Positive evidence of an atmosphere was 
sought in vain. Supposed volcanoes were traced to bright 



THE MOON. 



319 



spots, illuminated by light from the earth. Inequalities. of 
surface there were ; but in form they were wholly different 
from the mountains of the earth. So the beautiful fancies of 







_^ n 


. -^to^r^?PBHnS 


.ftSt- / 




i 


r 


■ .. .■ * ' > 

3 


... 

.... .V 

! o >4 


w 




BfL .r" '!'. .IMW 




> / 






1 


1 i ■ 

■ 


ft 


• 
• 

• 


% 


^ 


k 


m 


• - 

-« 



Fig. 80.— View of moon near the third quarter. From a photograph by Professor Henry 

Draper. 

the earlier astronomers all faded away, leaving our satellite as 
lifeless as an arid rock. 

As the moon is now seen and mapped, the difference be- 
tween the light and dark portions is due merely to a differ- 
ence in the color of the material, much of which seems to be 

oo 



320 THE SOLAR SYSTEM. 

darker than the average of terrestrial objects. The mountains 
consist, for the most part, of round saucer-shaped elevations, 
the interior being flat, with small conical mounds rising here 
aud there. Sometimes there is a single mound in the centre. 
It is very curious that the figures of these inequalities in the 
lunar surface can be closely imitated by throwing pebbles 
upon the surface of some smooth plastic mass, as mud or 
mortar. They may be well seen during an eclipse of the sun, 
when the contrast between the smoothness of the sun's limb 
and the roughness of that of the moon cannot escape notice. 
Their appearance is most striking when the eclipse is annular 
or total. In the latter case, as the last streak of sunlight is 
disappearing, it is broken up into a number of points, which 
have been known as " Baily's beads," from the observer who 
first described them, and which are caused by the sun shining 
through the depressions between the lunar mountains. 

To give the reader an idea what the formation of the lunar 
surface is, we present a view of the spot or crater " Coper- 
nicus," by Secchi, taken from the " Memoirs of the Royal As- 
tronomical Society," vol. xxxii. The diameter of the central 
portion, so much like a fort, is about 45 or 50 miles. 

Among the most curions and inexplicable features of the 
moon's surface are the long narrow streaks of white* material 
which radiate from certain points, especially from the great 
crater Tycho. Some of these can be traced more than a 
thousand miles. The only way in which their formation has 
been accounted for is by supposing that in some former age 
immense fissures were formed in the lunar surface which were 
subsequently filled by an eruption of this white matter which 
forms the streaks. 

Has the Moon an Atmosphere? — This question may be an- 
swered by saying that no evidence of a lunar atmosphere 
entitled to any weight has ever been gathered, and that if 
there is such an atmosphere, it is certainly not ^-J-jj- part the 
density of the earth's atmosphere. The most delicate known 
test of an atmosphere is afforded by the behavior of a star 
when in apparent contact with the limb of the moon. In this 



THE MOON. 



321 




position the rays of light coming from the star would pass 
through the lunar atmosphere, and be ref meted by twice the 
horizontal refraction of that atmosphere. The star would 
then be apparently thrown out of its true position in the di- 
rection from the moon's centre by the amount of this double 
refraction. But observations of stars in this position, at the 
moment when the limb of the moon passes over them, have 
never indicated the slightest displacement. It is certain that, 
had the displacement been decidedly in excess of half a sec- 
ond, it would have been detected ; therefore, the double hori- 
zontal refraction of the lunar atmosphere, if any exist, must 
be as small as half a second.* The corresponding refraction 
of the earth's atmosphere is 4000 seconds. Therefore, the re- 



* A similar test is afforded by the occultation of a planet, especially Saturn or 
Venus, the limb of which would be a little flattened as it touched the moon. The 
writer looked very carefully for this appearance during an unusually favorable oc- 
cultation of Saturn which occurred on Aug. 6th, 1876, without seeing a trace of it. 



322 THE SOLAR SYSTEM. 

fractive power of the lunar atmosphere cannot be much in ex- 
cess of -g-oV tf that of the earth's, and certainly falls below -5-^. 

Without an atmosphere no water or other volatile fluid can 
exist on the moon, because it would gradually evaporate and 
form an atmosphere of its own vapor. The evaporation would 
not cease till the pressure of the vapor became equal to its 
elastic force at the mean temperature of the moon. If this 
temperature were as low as the freezing-point, the pressure of 
an atmosphere of water vapor would be yj^ that of our at- 
mosphere. So dense an envelope could not fail of detection 
with our present means of observation. 

The question whether any change is taking place on the 
surface of the moon is one of interest. Hitherto, the pre- 
ponderance of evidence has been against the idea of any 
change. It is true that a few years ago there was a great 
discussion in the astronomical world about a supposed change 
in the aspect of the spot Linnaeus, which was found not to 
present the same appearance as on Beer and Madler's map. 
But careful scrutiny showed that, owning to some peculiarity 
of its surface, this spot varied its aspect according to the 
manner in which it was illuminated by the sun, and these 
variations appear to be sufficient to account for the supposed 
change. To whatever geological convulsions the moon may 
have been subjected in ages past, it seems as if she had now 
reached a state in which no further change was to take place, 
unless by the action of some new cause. This will not seem 
surprising if we reflect what an important part the atmosphere 
plays in the changes which are going on on the surface of the 
earth. The growth of forests, the formation of deltas, the 
w r ashing-away of mountains, the disintegration and blacken- 
ing of rocks, and the decay of buildings, are all due to the 
action of air and water, the latter acting in the form of rain. 
Changes of temperature powerfully re-enforce the action of 
these causes, but are not of themselves sufficient to produce 
any effect. Now, on the moon, there being neither air, wa- 
ter, rain, frost, nor organic matter, the causes of disintegra- 
tion and decay are all absent. A marble building erected 



THE MOON. 323 

upon the surface of the moon would remain century after 
century just as it was left. It is true that there might be 
bodies so friable that the expansions and contractions due to 
the great changes of temperature to which the surface of the 
moon is exposed would cause them to crumble. But whatev- 
er crumbling might thus be caused would soon be done with, 
and then no further change would occur. 

Light and Heat of the Moon. — That the sun is many times 
brighter than the moon is evident to the eye ; but no one 
judging by the unaided eye would suppose the disparity to be 
so great as it really is. It is found by actual trial that the 
light of the sun must be diminished several hundred thousand 
times before it becomes as faint as the full moon. The results 
of various experiments range between 300,000 and 800,000. 
Professor G. JB. Bond, of Cambridge, found the ratio to be 
470,000. The most careful determination yet made is by 
Zollner, who finds the sun to give 619,000 times as much 
light as the full moon. This result is probably quite near 
the truth. 

The moon does not shine by sunlight alone. Whenever 
the narrow crescent of the new moon is seen through a clear 
atmosphere, her whole surface may be plainly seen faintly il- 
luminated. This appearance is known as " the old moon in 
the new moon's arms." The faint light thus shed upon the 
dark parts of the moon is reflected from the earth. An ob- 
server on the moon would see the earth in his sky as a large 
moon, much larger than the moon is seen by us. When it is 
new moon with us, it would befall earth, if we may be allowed 
the term, to an observer on this side of the moon. Hence, 
under those circumstances, most of the lunar hemisphere hid- 
den by the sun is illuminated by earth-light, or by sunlight re- 
flected by the earth, and is thus rendered visible. The case 
is the same as if an observer on the moon should see the dark 
hemisphere of the earth by the light of the full moon. 

As the moon reflects the light of the sun, so also must she 
reflect his heat. Besides, she must radiate off whatever heat 
she absorbs from the sun. Hence, we must receive some heat 



324 THE SOLAR SYSTEM. 

from the moon, though calculation will show the quantity to 
be so small as to defy detection with the most delicate ther- 
mometer, the average quantity being only a 6 \ 6 part of that 
received from the sun. As the direct rays of the sun will not 
raise the black-bulb thermometer more than 50 or 60 degrees 
above the temperature of the air, those of the moon cannot 
raise it more than sVtht of a degree. By concentrating the 
rays in the focus of a telescope of large aperture and compar- 
atively short focal length, the temperature might be increased 
a hundred times or more ; but even then we should only have 
an increase of -^ of a degree. Even this increase might be 
unattainable, for the reason that the heat radiated by the 
moon would not pass through glass. It is, therefore, only 
since the discovery of therino electricity and the invention of 
the thermo-electric pile that the detection of the heat from 
the moon has been possible. The detection is facilitated by 
using a reflecting telescope to concentrate the lunar rays, 
because the moon is not hot enough to radiate such heat as 
will penetrate glass. Lord Rosse and M. Marie - Davy, of 
Paris, have thus succeeded in measuring the heat emanating 
from the moon. The former sought not merely to determine 
the total amount of heat, but how much it varied from one 
phase of the moon to the other, and what portion of it was 
the reflected heat of the sun, and what portion was radiated 
by the moon herself, as if she were a hot body. He found 
that from new to full moon, and thence round to new moon 
again, the quantity of heat received varied in the same way 
with the quantity of light ; that is, there was most at full- 
moon, and scarcely any when the moon was a thin crescent. 
That only a small proportion of the total heat emitted was the 
reflected heat of the sun, was shown by the fact that while 86 
per cent, of solar heat passes through glass, only 12 per cent, 
of lunar heat does so. This absorption by glass is well known 
to be a property of the heat radiated by a body which is not 
itself at a high temperature. The same result was indicated 
in another way, namely, that while the sun is found by Zoll- 
ner to give 618,000 times as much light as the moon, it only 



THE MOON. 325 

gives 82,600 times as much heat. Thus both the ratio of solar 
to lunar heat, and the proportion of the latter which is ab- 
sorbed by glass, agree in indicating that about six-sevenths of 
the heat received from the moon is radiated by the latter, 
owing to the temperature of her surface produced by the ab- 
sorption of the sun's rays. 

Lord Eosse was thus enabled to estimate the change of 
temperature of the moon's surface according as it was turned 
towards or from the sun, and found it to be more than 500° 
Fahrenheit. But there was no way of determining the tem- 
peratures themselves with exactness. Probably when the sun 
does not shine the temperature is two or three hundred de- 
grees below zero, and therefore below any ever known on the 
earth; while under the vertical sun it is as much above zero, 
and therefore hotter than boiling water. 

Effect of the Moon on the Earth. — We have already explained, 
in treating of gravitation, how the attraction of the moon 
causes tides in the ocean. This is one of the best-known ef- 
fects of lunar attraction. It is known from theory that a sim- 
ilar tide is produced in the air, affecting the height of the ba- 
rometer ; but it is so minute as to be entirely masked by the 
changes constantly going on in the atmospheric pressure from 
other causes. There is also reason to believe that the occur- 
rence of earthquakes may be affected by the attraction of the 
moon ; but this is a subject which needs further investiga- 
tion before we can pronounce with certainty on a law of con- 
nection. 

Thus far there is no evidence that the moon directly affects 
the earth or its inhabitants in any other way than by her at- 
traction, which is so minute as to be entirely insensible except 
in the ways We have described. A striking illustration of the 
fallibility of the human judgment when not disciplined by sci- 
entific training is afforded by the opinions which have at vari- 
ous times obtained currency respecting a supposed influence 
of the moon on the weather. Neither in the reason of the 
case nor in observations do we find any real support for such 
a theory. It must, however, be admitted that opinions of this 



326 



THE SOLAR SYSTEM. 



character are not confined to the uneducated. In scientific 
literature several papers are found in which long series of me- 
teorological observations are collated, which indicate that the 
mean temperature or the amount of rain had been subject to 
a slight variation depending on the age of the moon. But 
there was no reason to believe that these changes arose from 
any other cause than the accidental vicissitudes to which the 
weather is at all times subject. There is, perhaps, higher au- 
thority for the opinion that the rays of the full moon clear 
away clouds ; but if we reflect that the effect of the sun it- 
self in this respect is not very noticeable, and that the full 
moon gives only -g-owo 6f the heat of the sun, this opinion 
will appear extremely improbable. 

§ 6. The Planet Mars. 

The fourth planet in the order of distance from the sun, 
and the next one outside the orbit of the earth, is Mars. Its 
mean distance from the sun is about 141 millions of miles. 
The eccentricity of its orbit is such that at perihelion it is only 
128 millions of miles from the sun, while in aphelion it is 154 
millions distant. It is, next to Mercury, the smallest of the 
primary planets, its diameter being little more than 4000 
miles. It makes one revolution in its orbit in less than two 
years (more nearly in 687 days, or 43 J days short of two Ju- 
lian years). If the period were exactly two years, it would 
make one revolution while the earth made two, and the oppo- 
sitions would occur at intervals' of two years. But, going a 
little faster than this, it takes the earth, on the average, fifty 
days over the two years 'to catch up to it. The times of oppo- 
sition are shown in the following table: 



1873 April 27th. 

1875 .., June 20th. 



1877 Septemher 5th. 

1879 November 12th. 



The times of several subsequent oppositions may be found 
with sufficient-exactness for the identification of the planet by 
adding two years and two months for every opposition, except 
during the spring months, when "Only one month is to be 



<v 



THE PLANET MARS. 327 

added. Oppositions will occur in January, 1882, and Febru- 
ary, 1884. At the times of opposition Mars rises when the 
sun sets, and may be seen during the entire night. 

Aspect of Mars. — Mars is easily recognized with the naked 
eye when near its opposition by its fiery-red light. It is much 
more brilliant at some oppositions than at others, but always 
exceeds an ordinary star of the first magnitude. The varia- 
tions of its brilliancy arise from the eccentricity of its orbit. 
and the consequent variations of its distance from the earth 
and the sun. The perihelion of Mars is in the same longitude 
in which the earth is on August 27th; and when an opposition 
occurs near that date, the planet is only 35 millions of miles 
from the earth. This is about the closest approach which the 
two planets can ever make. When an opposition occurs in 
February or March the planet is near its aphelion — 151 mill- 
ions of miles from the sun and 02 millions from the earth. 
The result of these variations of distance is that Mars is more 
than four times brighter when an opposition occurs in August 
or September than when it occurs in February or March. The 
opposition of 1877 (September 5th) is cpiite remarkable in this 
respect, as it occurs only nine days after the planet has passed 
its perihelion. At that time Mars will form a conspicuous 
object in the south-eastern sky during the early evening. 

Mars has been an interesting object of telescopic research 
from the fact that it is the planet which exhibits the greatest 
analogy with our earth. The equatorial regions, even with a 
small telescope, can be distinctly seen to be divided into light 
and dark portions, which some observers suppose to be conti- 
nents and oceans. Around each pole is a region of brilliant 
white, which the same class of astronomers suppose to be due 
to a deposit of snow. The outlines of the dark and light por- 
tions are sometimes so hard to trace as to give rise to the sus- 
picion of clouds in a Martial atmosphere. At the same time, 
a single look at Mars through a large telescope would convince 
most observers that these resemblances to our earth have a 
very small foundation in observation, the evidence being neg- 
ative rather than positive. It must be said in their favor that 



328 



THE SOLAR SYSTEM. 



if our earth were viewed at the distance at which we view 
Mars, and with the same optical power, it would present a 
similar telescopic aspect. But it is also possible that if the 

optical power of our tele- 
scopes were so increased 
that we could see Mars as 
from a distance of a thou- 
sand miles, the resemblances 
would all vanish as com- 
pletely as they did in the 
case of the moon. 

So many drawings of 
Mars in various positions 
have been made by the nu- 
merous observers who have 
studied it, that it has be- 

Fig. 82 The planet Mars on Jnne 23d, 1S75, at 10 . 

hours 45 minutes, as seen by Professor Holden COme possible to COUStrilct 
with the great Washington telescope. tolerably accurate maps of 

the surface of the planet. We give a copy of one of these 
sets of maps by Kaiser, the late Leyden astronomer. Kaiser 
does not pretend to call the different regions continents and 
oceans, but merely designates them as light and dark portions. 




UO 30 io to o 




Jl) HI 1(1 Mil 31,0 330 320 3/0 3110 210 ISO Do ICO tiO 2U0 230 2!0 HO 200 ISO rSO TIO IOO ISO ttO 130 120 110 100 SO 30 10 00 SO kO 10 , 

Fig. 83 Map of Mars, after Kaiser, on Mercator's projection. 

Rotation of Mars. — Mars is the only planet besides the earth 
of which we can be sure that the time of axial rotation ad- 
mits of being determined with entire precision. Drawings by 
Hooke, two centuries ago, exhibit markings which can still be 
recognized, and from a comparison of them with recent ones 
Mr. Proctor has found for the period of rotation 24 hours 37 



THE PLAXET MAES. 



329 



minutes 22.73 seconds, which lie considers correct within three 
or four hundredths of a second. The equator of Mars is in- 
clined to the plane of its orbit about 27°,so that the vicissitudes 
of the seasons are greater on Mars than on the eartli in the pro- 
portion of 27° to 23£°. Owing to this great obliquity, we can 
sometimes see one pole of the planet, and sometimes the other, 
from the earth. When in longitude 350°, that is, in the same 




Sao of* 

Fig. 84.— Northern hemisphere of Mars. Fig. S5.— Southern hemisphere of Mars. 

direction from the sun in which the eartli is situated on Sep- 
tember 10th, the south pole of the planet is inclined towards 
the sun ; and if the planet is then in opposition, it will be in- 
clined towards the earth also, so that we can see the region of 
the planet to a distance of 27° beyond the pole. At an op- 
position in March the north pole of the planet is inclined tow- 
ards the sun, and towards the earth also. We have just seen 
that Mars is much farther at the latter oppositions than at the 
former, so that we can get much better views of the south pole 
of the planet than of the north pole. 

Satellites of Mars. — On the night of August 11th, IS 77. 
Professor Asaph Hall, while scrutinizing the neighborhood of 
Mars with the great equatorial of the Washington Observato- 
ry, found a small object about SO seconds east of the planet. 
Cloudy weather prevented further observation at that time; 
but on the night of the 16th it was again found, and two 
hours' observation showed that it followed the planet in its 



330 THE SOLAR SYSTEM. 

orbital motion. Still, fearing that it might be a small planet 
which chanced to be in the neighborhood, Professor Hall 
waited for another observation before announcing his discov- 
ery. A rough calculation from the observed elongation of the 
satellite and the known mass of Mars showed that the period 
of revolution would probably be not far from 29 hours, and 
that, if the object were a satellite, it would be hidden during 
most of the following night, but would reappear near its orig- 
inal position towards morning. This prediction was exactly 
fulfilled, the satellite emerging from the planet about four 
o'clock on the morning of August 18th. 

But this was not all. The reappearance of the satellite was 
followed by the appearance of another object, much closer to 
the planet, which proved to be a second and inner satellite. 
The reality of both objects was abundantly confirmed by obser- 
vations on the following nights, not only at Washington, but at 
the Cambridge Observatory, by Professor Pickering and his as- 
sistants, and at Cambridgeport, by Messrs. Alvan Clark & Sons. 

The most extraordinary feature of the two satellites is the 
proximity of the inner one to the planet, and the rapidity of 
its revolution. The shortest period hitherto known is that of 
the inner satellite of Saturn — 22 hours 37 minutes. But the 
inner satellite of Mars goes round in 7 hours 38 minutes. Its 
distance from the centre of the planet is about 6000 miles, 
and from the surface less than 4000. If there are any as- 
tronomers on Mars with telescopes and eyes like ours, they 
can readily find out whether this satellite is inhabited, the dis- 
tance being less than one-sixtieth that of the moon from us. 

That kind of near approach to simple relationships between 
the times of revolution is found here which we see in the sat- 
ellites of Jupiter and Saturn. The inner satellite of Mars re- 
volves in very nearly one-fourth the period of the outer one, 
these times being, Hre Min 

Outer satellite 30 18 

One-fourth this period 7 34£ 

Period of inner satellite 7 39 

These satellites may also be put down as by far the smallest 



THE SMALL PLANETS. 



331 



heavenly bodies yet known. It is hardly possible to make 
anything like a numerical estimate of their diameters, because 
they are seen in the telescope only as faint points of light ; 
and, having no sensible surface, no such thing as a measure 
of the diameters is possible. The only datum on which an 
estimate can be founded is the amount of light which they 
give. The writer judged the magnitude of the outer one to 
be between the eleventh and twelfth. According to the esti- 
mate of Zollner, Mars itself, at this opposition, is three magni- 
tudes brighter than a first-magnitude star. The difference of 
brilliancy between Mars and the outer satellite is, therefore, 
represented by thirteen or fourteen orders of magnitude. 
From this, it would follow that Mars gives from 200,000 to 
500,000 times as much light as the satellite ; and if both are of 
the same light-reflecting power, the diameter of the satellite 
would be from 6 to 10 miles. It may be as small as 5 miles, 
or as great as 20, but is not likely to lie far without these 
limits. The inner satellite is much brighter than the outer 
one, and its diameter probably lies between 10 and 40 miles. 




Fiu. S5u.— Apparent orbits of the satellites of Mars in 1ST7, as observed aud laid down by 

Professor Hall. 

§ 7. The Small Planets. 

It was impossible to study the solar system, as it was known 
to modern astronomy before the beginning of the present cen- 
tury, without being struck by the great gap which existed be- 
tween Mars and Jupiter. Except this gap, all the planets then 
known succeeded each other according to a tolerably regular 



332 THE SOLAR SYSTEM. 

law, and by interpolating a single planet at nearly double the 
distance of Mars the order of distances would be complete. 
The idea that an unknown planet might really exist in this 
region was entertained from the time of Kepler. So sure 
were some astronomers of this that, in 1800, an association of 
twenty-four observers was formed, having for its object a sys- 
tematic search for the planet. The zodiac was divided into 
twenty-four parts, one of which was to be searched through 
by each observer. But by one of those curious coincidences 
which have so frequently occurred in the history of science, 
the planet was accidentally discovered by an outside astrono- 
mer before the society could get fairly to work. On January 
1st, 1801, Piazzi, of Palermo, found a star in the constellation 
Taurus which did not belong there, and on observing it the 
night after, he found that it had changed its position among 
the surrounding stars, and must, therefore, be a planet. He 
followed it for a period of about six weeks, after which it was 
lost in the rays of the sun without any one else seeing it. 
When it was time to emerge again in the following autumn, 
its rediscovery became a difficult problem. But the skill of the 
great mathematician Gauss came to the rescue with a method 
by which the orbit of any planetary body could be complete- 
ly and easily determined from three or four observations. He 
was thus able to tell observers where their telescopes must be 
pointed to rediscover the planet, and it was found without dif- 
ficulty before the end of the year. Piazzi gave it the name 
Ceres. The orbit found by Gauss showed it to revolve between 
Mars and Jupiter at a little less than double the distance of 
the former, and therefore to be the long -thought -of planet. 
But the discovery had a sequel which no one anticipated, and 
of which we have not yet seen the end. In March, 1802, 01- 
bers discovered a second planet, which was also found to be 
revolving between Mars and Jupiter, and to which he gave 
the name Pallas. The most extraordinary feature of its orbit 
was its great inclination, which exceeded 34°. Olbers there- 
upon suggested his celebrated hypothesis that the two bodies 
might be fragments of a single planet which had been shat- 



THE SMALL PLANETS. 333 

tered by some explosion. If such were the case, the orbit.- of 
all the fragments would at first intersect each other at the 
point where the explosion occurred. lie therefore thought it 
likely that other fragments would be found, especially if a 
search were kept up near the point of intersection of the orbit- 
of Ceres and Pallas. Acting on this idea, Harding, of Lilien- 
thal, found a third planet in 1804, while Olbers found a 
fourth one in 1807. These were called Juno and Vesta. The 
former came quite near to Olbers's theory that the orbit- 
should all pass near the same point, but the latter did not. 
Olbers continued a search for additional planets of this group 
for a number of years, but at length gave it up, and died 
without the knowledge of any but these four. 

In December, 1845, thirty-eight years after the discovery of 
Vesta, Ilencke, of Driesen, being engaged in the preparation 
of star-charts, found a fifth planet of the group, and thus re-, 
commenced a series of discoveries which have continued till 
the present time. No less than three were discovered in 1847. 
and at least one has been found every year since. To show 
the rate at which discovery has gone on, we divide the time 
since 1845 into periods of five years each, and give the num- 
ber found during each period : 



In 184f>-. r >0 


.... 8 were discovered. 


In 1861-65 


.... 23 were discovered. 


" 1861-55 


.... 24 " 


" 1866-70 


.... 27 " 


11 1856-60 


.... 25 " 


" 1871-75 


.... 45 " 



In 1876 twelve, and in 1877 eleven, were discovered, while seven additional ones 
have lieen found since the beginning of 1878, making a total of 187 known 
at the present time (May, 1878). 

It will be seen that the rate of discovery has been pretty 
steadilv increasing during thirty years. This is not because 
the number of those visible, but not yet found, is so great that 
it is as easy as ever to find one, but because they are now 
sought after with more skill and more system than formerly.* 

* In illustration of this the writer has been informed by Professor Peters that 
in searching for these bodies he falls upon several already known for every new one 
that he finds. Consequently, were they all lost, he alone could now rediscover 
them at a more rapid rate than they actually have been discovered by the efforts 
of all the observers engaged in the search. 



334 THE SOLAR SYSTEM. 

Of those discovered during the last ten years, nearly half 
have been found by two American observers, Professors Pe- 
ters and Watson. American discoveries of these bodies were 
commenced by Mr. James Ferguson, who discovered Euphros- 
yne at Washington on September 1st, 1854. 

All the planets of this group are remarkable for their mi- 
nuteness. The disks are all so small as to defy exact meas- 
urement, presenting the appearance of mere stars. A rough 
estimate of their diameters can, however, be made from the 
amount of light which they reflect; and although, in the ab- 
sence of exact knowledge of their reflecting power, the results 
of this method are not very certain, they are the best we can 
obtain. It is thus found that Ceres and Vesta are the largest 
of the group, their diameters lying somewhere between 200 
and 400 miles ; while, if we omit some very lately discovered, 
the smallest are Atalanta, Maja, and Sappho, of which the di- 
ameters may be between 20 and 40 miles. We may safely 
say that it would take several thousand of the largest of these 
small planets to make one as large as the earth. 

It has sometimes been said that some of these bodies are of 
irregular shape, and thus favor Olbers's hypothesis that they 
are fragments of an exploded planet. But this opinion has 
no other foundation than a suspected variability of their light, 
which may be an illusion, and which, if it exists, might result 
from one side of the planet being darker in color than the 
other. The latter supposition is not at all improbable, as many 
of the satellites are known to be variable from this or some 
analogous cause. As the supposed irregularities of form have 
never been seen, and are not necessary to account for the va- 
riations of brilliancy, there is no sufficient reason for believing 
in their existence. 

Olbers's Hypothesis. — The question whether these bodies 
could ever have formed a single one has now become one of 
cosmogony rather than of astronomy. If a planet were shat- 
tered, the orbit of each fragment would, at first, pass through 
the point at which the explosion occurred, however widely 
they might be separated through the rest of their course. But 



THE SMALL PLANETS. 335 

owing to the secular changes produced by the attractions of 
the other planets, this coincidence would not continue. The 
orbits would slowly move away, and after the lapse of a few 
thousand years no trace of a common intersection would be 
seen. It is, therefore, curious that Olbers and his contempora- 
ries should have expected to find such a region of intersection, 
as it implied that the explosion had occurred within a few 
thousand years. The fact that the required conditions were 
not fulfilled was no argument against the hypothesis, because 
the explosion might have occurred millions of years ago, and 
in the mean time the perihelion and node of each orbit 
would have made many entire revolutions ; so that the orbits 
would have been completely mixed up. 

Desirous of seeing whether the orbits passed nearer a com- 
mon point of intersection in times past than at present, Encke 
computed their secular variations. The result seemed to be 
adverse to Olbers's hypothesis, as it showed that the orbits 
were farther from having a common point in ages past than 
at present. But this result was not conclusive either, because 
he only determined the rates at which the orbits are now 
changing, whereas, as previously explained, the orbits of all 
the planets really go through periodic oscillations ; and it is 
only by calculating these oscillations that their positions can 
be determined for very remote epochs. They have since 
been determined for some of the planets in question, and the 
result seems to show that the orbits could never have intersect- 
ed unless some of them have, in the mean time, been altered 
by the attraction of the small planets on each other. Such an 
action is not impossible; but it is impossible to determine it, 
owing to the great number of these bodies, and our ignorance 
of their masses. We can, however, say that if the explosion 
ever did occur, an immense interval, probably millions of 
years, must have elapsed in the mean time. A different ex- 
planation of the group is given by the nebular hypothesis, of 
which we shall hereafter speak, so that Olbers's hypothesis is 
no longer considered by astronomers. 

The planets in question are distinguished from the others, 

23 



336 THE SOLAR SYSTEM. 

not only by their small size, but by the great eccentricities 
and inclinations of their orbits. If we except Mercury, none 
of the larger planets has an eccentricity amounting to one- 
tenth the diameter of its orbit, nor is any orbit inclined more 
than two or three degrees to the ecliptic. But the inclina- 
tions of many of the small planets exceed ten degrees, and 
the eccentricities frequently amount to a fourth of the radii 
of their orbits. The result is that the same small planet is at 
very different distances from the sun in various points of its 
orbit. Add to this the fact that the mean distances of these 
bodies from the sun have a pretty wide range, and we shall 
find that they extend through a quite broad zone. The inside 
edge of this zone seems pretty well marked, its distance being 
about 180 millions of miles from the sun, or between 30 and 
40 millions beyond the orbit of Mars. On the outside, it ter- 
minates more gradually, but nowhere extends within 50 mill- 
ions of miles of the orbit of Jupiter. If any of the small 
planets ever ranged outside of certain limits, the attraction of 
Mars or Jupiter was so great as to completely derange their 
orbits, so that we have a physical law which sets a limit to the 
zone; but whether the limit thus set would coincide with the 
actual limit we cannot at present say. 

There are also within the limits of the group certain posi- 
tions, in which, if the orbits were placed, they would be greatly 
changed by the action of Jupiter. These positions are those 
in which the time of revolution would be some simple exact 
fraction of that of Jupiter, as J, -J, §, y, etc. Professor Daniel 
Kirkwood has pointed out the curious fact that there are gaps 
in the series of small planets corresponding to these periodic 
times. Whether these gaps are really due to the relations of 
the periodic times, or are simply the result of chance, cannot 
yet be settled. The fact that quite a number of the small 
planets have a period very nearly three-eighths that of Jupiter, 
may lead us to wait for further evidence before concluding 
that we have to deal with a real law of nature in the cases 
pointed out by Professor Kirkwood. 

Number and Total Mass of the Small Planets: — At present it 



THE SMALL PLANETS. 337 

is not possible to set any certain limits to the probable number 
of the small planets. Although a hundred and seventy-two 
are now known, there is as yet no sensible diminution in the 
rate at which they are being discovered. The question of 
their total number depends very largely on whether there is 
any limit to their minuteness. If there is no such limit, then 
there may be an indefinite number of them, too small to be 
found with the telescopes now engaged in searching for them; 
and the larger the telescopes engaged in the search, the more 
will be found. On the other hand, if they stop at a certain 
limit — say twenty miles in diameter — we may say with con- 
siderable confidence that their total number is also limited, 
and that by far the largest part of them wrtl be discovered 
by the present generation of astronomers. 

So far as we can now see, the preponderance of evidence is 
on the side of the number and magnitude being limited. The 
indications in this direction are that the newly discovered ones 
are not generally the smallest objects which could be seen 
with the telescopes which have made the discovery, and do 
not seem, on the average, to be materially smaller than those 
which were discovered ten years ago. It is not likely that the 
number of this average magnitude which still remain undis- 
covered can be very great, and new ones will probably be 
found to grow decidedly rare before another hundred are dis- 
covered. Then it will be necessary to employ greater optical 
power in the search. If this results in finding a number of 
new ones too small to be found with the former telescopes, we 
shall have to regard the group as unlimited in number. But 
if no sucji new ones are thus found, it will show that the end 
has been nearly reached. 

In gravitational astronomy, the question of the total mass 
of the small planets is more important than that of their total 
number, because on this mass depends their effect in altering 
the motions of the large planets. Any individual small planet 
is so minute that its attraction on the other planets is entirely 
insensible. But it is not impossible that the whole group 
might, by their combined action, produce a secular variation 



33 S THE SOLAR SYSTEM. 

in the form of the orbits of Mars and Jupiter which, in the 
course of years, will be clearly shown by the observations. 
But, although accurate observations of these planets have been 
made for more than a century, no such effect has yet been no- 
ticed. The sum total of their masses must, therefore, be much 
less than that of an average planet, though we cannot say pre- 
cisely what the limit is. The apparent magnitude of those 
which have been discovered is entirely accordant with the 
opinion that the mass of the entire group is so small that it 
cannot make itself felt by its attraction on the other planets 
for many years to come. In fact, if their diameters be esti- 
mated from their brightness, in the manner already indicated, 
we shall iind that if all that are yet known were made into a 
single planet the diameter would be less than 400 miles ; and 
if a thousand more, of the average size of those discovered 
since 1850 should exist, their addition to the consolidated 
planet would not increase its diameter to 500 miles. Such a 
planet would be onty tttott of the bulk of the earth, and, un- 
less we supposed it to possess an extraordinary specific gravity, 
could not much exceed ^Vo of the mass of the earth, or -^ of 
the mass of Mercury. We may fairly conclude that unless 
the group of small planets actually consists of tens of thou- 
sands of minute bodies, of which only a few of the brightest 
have yet been discovered, their total volume and mass are far 
less than those of any one of the major planets. 

The number of these bodies now known is so great that the 
mere labor of keeping the run of their motions, so that they 
shall not be lost, is out of proportion to the value of its results. 
It is mainly through the assiduity of German students that 
most of them are kept from being lost. Should many more 
be found, it may be necessary to adopt the suggestion of an 
eminent German astronomer, and let such of them as seem 
unimportant go again, and pursue their orbit undisturbed by 
telescope or computer. 



THE PLANET JUPITER, 339 



CHAPTER IV. 

THE OUTER GROUP OF PLANETS. 

§ 1. The Planet Jupiter. 

Jupiter is the "giant planet " of onr system, li is mass large- 
ly exceeding that of all the other planets combined. His 
mean diameter is about 85,000 miles; but owing to his rapid 
rotation on his axis, his equatorial exceeds his polar diameter 



Fig. 86.— Jupiter as seen with the great Washington telescope, March 21st, 1876. 15 hours 
38 minutes mean time. Drawn by Professor Holdeu. 

by 5000 miles. In volume he exceeds our earth about 1300 
times, while in mass he exceeds it about 213 times. His spe- 
cific gravity is, therefore, far less than that of the earth, and 
even less than that of water. His mean distance from the 
sun is 4S0 millions of miles, but, owing to the eccentricity of 
his orbit, his actual distance ranges between 457 and 503 mill- 
ions. His time of revolution is fifty days less than twelve 
years. 



340 THE SOLAR SYSTEM. 

Jupiter is easily recognized by his brilliant white light, with 
which he outshines every other planet except Venus. To fa- 
cilitate his recognition, we give the dates of opposition dur- 
ing a few years. 

1877 June 19th. I 1879 August 31st. 

1878 July 25th. i 1880 ....October 7th, 

During the four years following 1880 he will be in opposition, 
on the average, about a month and seven days later each year; 
namely, in the middle of November, 1881 ; towards the latter 
part of December, 1882, and so on. A month or two before 
opposition he can be seen rising late in the evening, while 
during the three months following opposition he will always 
be seen in the early evening somewhere between south-east 
and south-west. 

The Surface of Jupiter. — Except the sun and moon, there is 
no object of our system which has during the last few years 
been the subject of more careful examination than this planet. 
Unlike Mars, there are no really permanent markings on his 
surface, and a map of Jupiter is therefore impossible. But 
this surface always presents a very diversified appearance. 
The earlier telescopic observers described light and dark belts 
as extending across it. Until a quite recent period, it has 
been customary to describe these belts as two in number, one 
north of the equator, and the other south of it. Commonly, 
they are seen as dark bands on the bright disk of the planet ; 
but it is curious that Huyghens represents them as brighter 
than the rest of the surface. As telescopic power was in- 
creased, it was seen that these so-called bands were of a far 
more complex structure than had been supposed, and consisted 
of great numbers of stratified, cloud-like appearances of the 
most variegated forms. These forms change so rapidly that 
the face of the planet hardly ever presents the same appear- 
ance on two successive nights. They are most strongly 
marked at some distance on each side of the Jovian equator, 
and thus give rise to the appearance of two belts when a very 
small or imperfect telescope is used. 



THE PLANET JUPITER. 341 

Both the outlines of these belts and the color of some parts 
of the planet, seem subject to considerable changes. The 
equatorial regions, and indeed the spaces between the belts 
generally, are often of a rosy tinge. This coloring is some- 
times so strongly marked as to be evident to the most super- 
ficial observer, while at other times hardly a trace of it can be 
seen. 

Spots which are much more permanent than the ordinary 
markings on the belt are sometimes visible. By watching 
these spots from day to day, and measuring their distance 
from the apparent disk, the time of rotation of Jupiter on hie 
axis has been determined. Commonly the spots are dark ; 
but on some rather rare occasions the planet is seen with a 
number of small, round, bright spots like satellites. Of these 
bright spots no explanation has been given. 




Fig. 87.— View of Jupiter, as seen in Lord Rosse's great telescope on February 27th, 
1S61, at 12 hours 30 minutes. 

From the changeability of the belts, and indeed of nearly all 
the visible features on the surface of Jupiter, it is clear that 
what we see on that planet is not the surface of a solid nu- 
cleus, but vaporous or cloud-like formations which cover the 
entire surface and extend to a great depth below. To all ap- 
pearance, the planet is covered with a deep and dense atmos- 



342 THE SOLAR SYSTEM. 

phere, through which light cannot penetrate on account of 
thick masses of clouds and vapor. In the arrangements of 
these clouds in streaks parallel to the equator, and in the 
change of their forms with the latitude, there may be some- 
thing analogous to the zones of clouds and rain on the earth. 
But of late years it has been noticed that the physical consti- 
tution of Jupiter seems to offer more analogies to that of the 
sun than to that of the earth. Like the sun, he is brighter in 
the centre than near the edges. This is shown in the most- 
striking manner in the transits of his satellites over his disk. 
When the satellite first enters on the disk, it commonly seems 
like a bright spot on a dark background ; but as it approaches 
the centre, it appears like a dark spot on the bright back- 
ground of the planet. The brightness of the centre is prob- 
ably two or three times greater than that of the limb. This 
diminution of light towards the edge may arise, as in the case 
of the sun, from the light near the edge passing through a 
greater depth of atmosphere, and thus becoming fainter by 
absorption. 

A still more remarkable resemblance to the sun has some- 
times been suspected — nothing less, in fact, than that Jupiter 
shines partly by his own light. It was at one time supposed 
that he actually emitted more light than fell upon him from 
the sun ; and if this were proved, it would show conclusive- 
ly that he was self-luminous. If all the light which the sun 
shed upon the planet were equally reflected in every direction, 
we might speak with some certainty on this question ; but in 
the actual state of our knowledge we cannot. Zollner has 
found that the brightness of Jupiter may be accounted for by 
supposing him to reflect 62 per cent, of the sunlight which he 
receives. But if this is his average reflecting power, the re- 
flecting power of his brighter portions must be much greater; 
in fact, they are so bright that they must shine partly by their 
own light, unless they reflect a disproportionate share of the 
sunlight back in the direction of the earth and sun. Clouds 
would not be likely to do this. On the other hand, if we as- 
sume that the planet emits any great amount of light, we are 
i 



THE PLANET JUPITER. 34:3 

met by the fact that, if this were the case, the satellites would 
shine by this light when they were in the shadow of the 
planet. As these bodies totally disappear in this position, the 
quantity of light emitted by Jupiter must be quite small. On 
the whole, there is a small probability that the brighter spots 
of this planet are from time to time slightly self-luminous. 

Again, the interior of Jupiter seems to be the seat of an 
activity so enormous that we can attribute it only to a very 
high temperature, like that of the sun. This is shown by the 
rapid movements always going on in his visible surface, which 
frequently changes its aspect in a few hours. Such a power- 
ful effect could hardly be produced by the rays of the sun, 
because, owing to the great distance of the planet, he receives 
only between one-twenty-fifth and one-thirtieth of the light 
and heat which we do. It is therefore probable that Jupiter 
is not yet covered by a solid crust, as our earth is, but that 
his white-hot interior, whether liquid or gaseous, has nothing 
to cover it but the dense vapors to which that heat gives rise. 
In this case the vapors may be self-luminous when they have 
.freshly arisen from the interior, and may rapidly cool off after 
reaching the upper limit to which they ascend. 

Rotation of Jupiter. — Owing to the physical condition of Ju- 
piter, no precisely determinate time of rotation can be assign- 
ed him, as in the case of Mars. Without a solid crust which 
we can see from time to time, the observed times of rota- 
tion will be those of liquid or vaporous formations, which may 
have a proper motion of their own. A spot has, however, on 
some occasions been observed for several months, and it has 
thus been pretty certainly determined that the time of rota- 
tion is about 9 hours 55-J minutes. The first observation of a 
spot of this kind was made by Cassini, who found the time of 
rotation to be 9 hours 55 minutes 58 seconds. No further 
exact observations were made until the time of Sehroter, who 
observed a number of transient spots during 17S5 and 17S6. 
The times of rotation varied from 9 hours 55 minutes to 9 
hours 56 minutes, from which he concluded that heavy storms 
raged on the surface of the planet, and gave the cloudy masses 



3J:4 THE SOLAR SYSTEM. 

which formed the spots a motion of their own. In Novem- 
ber, 1S34, a remarkable spot was observed by Madler, of Dor- 
pat, which lasted until the following April, from which the 
time of rotation came out 9 hours 55 minutes 30 seconds; but 
the observations showed that the spot did not move uniformly. 
Professor Airy, who observed the same spot at Cambridge, 
found the period to be 9 hours 55 minutes 21.3 seconds. 

Recent observations and researches indicate that the equa- 
torial regions of Jupiter rotate in less time, and with more ir- 
regularity, than the others, thus showing still another analogy 
between that planet and the sun. Thus, in 1871, Dr. Lohse, 
of Bothkamp, observed a spot near Jupiter's equator, which 
during several days performed its revolution in a period of 
9 hours 51 minutes 47 seconds. Other equatorial spots had a 
very irregular motion, but their period was generally less than 
that found by Madler and Airy. 

§ 2. The Satellites of Jupiter. 

One of the earliest telescopic discoveries by Galileo was 
that Jupiter was accompanied by four satellites, which re- 
volved round him as a centre, thus forming a miniature copy 
of the solar system. As in the case of spots on the sun, Gal- 
ileo's announcement of this discovery was received with in- 
credulity by those philosophers of the day who believed that 
everything in nature was described in the writings of Aris- 
totle. One eminent astronomer — Clavius — said that to see 
the satellites one must have a telescope which would produce 
them; but he changed his mind as soon as he saw them him- 
self. Another philosopher, more prudent, refused to put his 
eye to the telescope lest he should see them and be con- 
vinced. He died shortly afterwards. " I hope,'' said the caus- 
tic Galileo, " that he saw them while on his way to heaven." 

A very small telescope, or even a good opera-glass, is suf- 
ficient to show these bodies. Indeed, very strong evidence is 
on record that they have been seen with the naked eye. That 
they could be seen by any good eye, if the planet were out of 
the way, there is no doubt, the difficulty in seeing them aris- 



THE SATELLITES OF JUT ITER. 345 

ing from the glare of the planet on the eve. If the lenses of 
the eye are so transparent and pure that there is no such 
glare, it is quite possible that the two outer satellites might 
be seen, especially if they should happen to be close to- 
gether. 

According to the best determinations, which are, however, 
by no means certain, the diameters of the satellites of Jupiter 
range between 2200 and 3700 miles, the third from the planet 
bein<£ the largest, and the second the smallest. The volume of 
the smallest is, therefore, very near that of our moon. 

The light of these satellites varies to an extent which it 
is difficult to account for, except by supposing very violent 
changes constantly going on on their surfaces. It has some- 
times been supposed that some of them, like our moon, always 
present the same face to Jupiter, and that the changes in their 
brilliancy are due to differences in the color of the parts of 
the satellites which are successively turned towards us during 
one revolution round the planet. But the careful measures 
of their light made by Auwers, of Berlin, and Engelniann. of 
Leipsic, show that this hypothesis does not account for the 
changes of brilliancy, which are sometimes sudden in a sur- 
prising degree. The satellites are so distant as to elude tele- 
scopic examination of their surfaces. AVe cannot, therefore, 
hope to give any certain explanation of these changes. 

The satellites of Jupiter offer problems of great difficulty 
to the mathematician who attempts to calculate the effect of 
their mutual attractions. The secular variations of their or- 
bits are so rapid that the methods applied in the case of the 
planets cannot be applied here without material alterations. 
The most curious and interesting effect of their mutual at- 
traction is that there is a connection between the motions of 
the three inner satellites such as exists nowhere else in the 
solar system. The connection is shown by these two laws : 

1. That the mean motion of the first satellite added to twice the 
mean motion of the third is exactly equal to three times the mean 
motion of the second. 

2. That if to the mean longitude of the first satellite ice add 



3±6 THE SOLAR SYSTEM. 

twice the mean longitude of the third, and subtract three times the 
mean longitude of the second, the difference is always 180°. 

The first of these relations is shown in the following table 
of the mean daily motions of the satellites: 

Satellite I. in one day moves 203°.4890 

II. " " 101°.3748 

" III. " " 50°. 31 77 

" IV. " " 21°.571L 

Motion of Satellite 1 203\4890 

Twice that of Satellite III , 100°. 6354 

Sum 304°.1244 

Three times motion of Satellite II 304°. 1244 

It was first found from observations that the three satellites 
moved together so nearly according to this law that no certain 
deviation could be detected. But it was not known whether 
this was a mere chance coincidence, or an actual law of nat- 
ure, till Laplace showed that, if they moved so nearly in this 
way as observations had shown them to, there would be an ex- 
tremely minute force arising from their mutual gravitation, 
sufficient to keep them in this relative position forever. There 
is, in this case, some analogy to the rotation of the moon, 
which, being once started presenting the same face to the 
earth, is always held in that position by a minute residual of 
the earth's attraction. 

We have already spoken of the discovery of the progressive 
motion of light from the eclipses of these satellites, and of 
the uses of these eclipses for the rough determination of 
longitudes. Both the eclipses, and the transits of their bodies 
over the face of Jupiter afford interesting subjects of obser- 
vation with a telescope of sufficient power, say four inches ap- 
erture or upwards. To facilitate such observations the times 
of these phenomena are predicted in both the American and 
British Nautical Almanacs. 

§ 3. Saturn and its System, Physical Aspect, Belts, Rotation. 

Saturn is the sixth of the major planets in the order of dis- 
tance from the sun, around which it revolves in 29J years at 



SATURN AND IIIS SYSTEM. 



347 



a mean distance of about 880 millions of miles. In mass and 
size it stands next to Jupiter. To show the disparity in the 
masses of the planets we may refer to the table already given, 
showing that although Saturn is not one -third the mass of 
Jupiter, it has about three times the mass of the six planets, 
which are smaller than itself put together. Its surroundings 
are such as to make it the most magnificent object in the solar 
system. While no other planet is known to have more than 




Fig. S8.— View of Saturn and his rings. 

four satellites, Saturn has no less than eight. It is also sur- 
rounded by a pair of rings, the interior diameter of which is 
about 100,000 miles. The aspect of these rings is subject to 
great variations, for reasons which w T ill soon appear. The 
great distance of the planet renders the study of its details 
difficult unless the highest telescopic power is applied. The 
whole combination of Saturn, his rings, and his satellites is 
often called the Saturnian System. 

The planet Saturn generally shines with the brilliancy of a 



348 THE SOLAR SYSTEM. 

moderate first-magnitude star, and with a dingy, reddish light, 
as if seen through a smoky atmosphere. Its apparent bright- 
ness is, however, different at different times : during the years 
1876-1879 it is fainter than the average, owing to its ring be- 
ing seen nearly edgewise. From 1878 till 1885 it will con- 
stantly grow brighter, on account both of the opening out of 
the ring and the approach of the planet to its perihelion. 
The times of opposition are as follow : 

1877 September 9th. I 1879 October 5th. 

1878 September 22d. I 1880 October 18th. 

In subsequent years opposition will occur about thirteen days 
later every year, so that by adding this amount to the date for 
each year the oppositions can be found until the end of the 
century without an error of more than a few days. 

The physical constitution of Saturn seems to bear a great 
resemblance to that of Jupiter ; but, being twice as far away, 
it cannot be so well studied. The farther an object is from 
the sun, the less brightly it is illuminated ; and the farther 
from the earth, the smaller it looks, so that there is a double 
difficulty in getting the finest views of the more distant plan- 
ets. When examined under favorable circumstances, the sur- 
face of Saturn is seen to be diversified with very faint mark- 
ings ; and if high telescopic powers are used, two or more 
very faint streaks or belts may be seen parallel to its equator, 
the strongest ones lying on, or very near, the equator. As in 
the case of Jupiter, these belts change their aspect from time 
to time, but they are so faint that the changes cannot be 
easily followed. It is therefore, in general, difficult to say 
with certainty whether w r e do or do not see the same face of 
Saturn on different nights; and, consequently, it is only on 
extraordinary occasions that the time of rotation can be de- 
termined. 

The first occasion on which a well-defined spot was known 
to remain long enough on Saturn to determine the period of 
its rotation was in the time of Sir W. Herschel, who, from 
observations extending over several weeks, found the time of 



THE RINGS OF SAT U US'. 349 

rotation to be 10 hours 16 minutes.* No further opportu- 
nity for determining this period seems to have offered itself 
until 1876, when an appearance altogether new suddenly 
showed itself on the globe of this planet. On the evening of 
December 7th, 1876, Professor Hall, who had been engaged 
in measures of the satellites of Saturn with the great Wash- 
ington telescope, saw a brilliant white spot near the equator 
of the planet. It seemed as if an immense eruption of white- 
hot matter had suddenly burst up from the interior. The 
spot gradually spread itself out in the direction which would 
be east on the planet, so as to assume the form of a long light 
streak, of which the brightest point was near the following 
end. It continued visible until January, when it became faint 
and ill-defined, and the planet was lost in the rays of the suu. 
Immediately upon the discovery of this remarkable phenom- 
enon, messages were sent to other observers in various parts of 
the country, and on the 10th it was seen by several observers, 
who noted the time at which it crossed the centre of the disk 
in consequence of the rotation of the planet. From all the 
observations of this kind, Professor Hall found the period of 
Saturn to be 10 hours 14 minutes, taking the brightest part 
of the streak, which, as we have said, was near one end. 
Had the middle of the streak been taken, the time would have 
been less, because the bright matter seemed to be carried 
along in the direction of the planet's rotation. Attributing 
this to a wind, the velocity of the latter would have been be- 
tween 50 and 100 miles an hour. 

§ 4. The Rings of Saturn. 

The most extraordinary feature of Saturn is the magnificent 
system of rings by which he is surrounded. To the early 
telescopists, who could not command sufficient optical power 
to see exactly what it was, this feature was a source of great 

* It is very curious that nearly all modern writers give about 10 hours 29 min- 
utes as the time of rotation of Saturn which Herschel finally deduced. I can 
find no such result in Herschel's papers. A suspicious coincidence is that this 
period agrees with that assigned for the time of rotation of the ring. 



350 THE SOLAR SYSTEM. 

perplexity and difference of opinion. To Galileo it made the 
planet appear triform — a large globe with two small ones af- 
fixed to it, one on each side. After he had observed it for a 
year or two, he was greatly perplexed to find that the append- 
ages had entirely disappeared, leaving Saturn a single round 
globe, like the other planets. His chagrin was heightened by 
the fear, not unnatural under the circumstances, that the curi- 
ous form he had before seen might be due to some optical il- 
lusion connected with his telescope. It is said (I do not know 
on what authority) that his annoyance at the supposed decep- 
tion into which he had fallen was so great that he never again 
looked at Saturn. 

A very few years sufficed to show other observers, who had 
command of more powerful telescopes, that the singularity of 
form was no illusion, but that it varied from time to time. 
We give several pictures from Huyghens's Systema Saturnium, 
showing how it was represented by various observers during 
the first forty years of the telescope. If the reader will com- 
pare these with the picture of Saturn and his rings as they 
actually are, he will see how near many of the observers came 
to a representation of the proper apparent form, though none 
divined to what sort of an appendage the appearance was 
due. 

The man who at last solved the riddle was Huyghens, of 
whose long telescopes we have already spoken. Examining 
Saturn in March and April, 1655, he saw that instead of the 
appendages presenting the appearance of curved handles, as 
in previous years, a long narrow arm extended straight out on 
each side of the planet. The spring following, this arm had 
disappeared, and the planet appeared perfectly round as Gal- 
ileo had seen it in 1612. In October, 1655, the handles had 
reappeared, much as he had seen them a year and a half be- 
fore. To his remarkably acute mathematical and mechanical 
mind this mode of disappearance of the handles sufficed to 
suggest the cause which led to their apparent form. Waiting 
for entire confirmation by future observations, he communica- 
ted his theory to his fellow-astronomers in the following com- 



THE RINGS OF SATURN. 



> <©> 




Fio. 89. —Specimens of drawings of Saturn by various observers before the rings were 
recognized as such: I. Form as given by Galileo in 1610; II. Drawing by Scheiner. in 
1614, "showing ears to Saturn ;" III. Drawing by Ricciolus, in 1640 and 1643; IV.. V., 
VI., and VII. are by Hevelius, and show the changes due to the different angles under 
which the rings were seen; VIII. and IX. are by Ricciolus, between 1G4S aud 1660, 
when the ring was seen at the greatest an^le ; X. is by a Jesuit who passed under 
the pseudonym of Eustachhis de Divinis; XI. is by Fontana ; XIL by Gasseudi and 
Blaucanus, and XIII. by Ricciolus. 

bination of letters, printed without explanation at the end of a 
little pamphlet on his discovery of the satellite of Saturn : 

aaaaaaa ccccc d eeeee g h iiiiiii llll mm nnnnnnnnn oooo pp q rr s ttttt uuuuu, 

which, properly arranged, read — 

" Annulo cingitur, tenui, piano, nusquam coh&rente, ad ecliptiram inclinato " 
(It is girdled by a thin plane ring, nowhere touching, inclined to the ecliptic). 

This description is remarkably complete and accurate ; and 
enabled Huyghens to give a satisfactory explanation of the 

24 



352 THE SOLAR SYSTEM. 

various phases which the ring had assumed as seen from the 
earth. Owino* to the extreme thinness and flatness of the ob- 
jeet, it was completely invisible in the telescopes of that time 
when its edge was presented towards the observer or towards 
the sun. This happens twice in each revolution of Saturn, in 
much the same way that the earth's equator is twice directed 
towards the sun in the course of the year. The ring is in- 
clined to the plane of the planet's orbit by 27°, corresponding 
to the angle of 23|-° between the earth's equator and the 
ecliptic. The general aspect from the earth is very near the 
same as from the sun. As the planet revolves around the 
sun, the axis and plane of the ring preserve the same absolute 
direction in space, just as the axis of the earth and the plane 
of the equator do. 

"When the planet is in one part of its orbit, an observer at 
the sun or on the earth will see the upper or northern side of 
the ring at an inclination of 27°. This is the greatest angle 
at which the ring can ever be seen, the position occurring 
when the planet is in 262° of longitude, in the constellation 
Sagittarius. When the planet has moved through a quarter 
of a revolution, the edge of the ring is turned towards the sun, 
and, owing to its extreme thinness, it is visible only in the 
most powerful telescopes as an exceedingly fine line of light, 
stretching out on each side of the planet. In this position the 
planet is in longitude 352°, in the constellation Pisces. When 
the planet has moved 90° farther, an observer on the sun or 
earth again sees the ring at an angle of 27° ; but now it is the 
lower or southern side which is visible. The planet is now in 
longitude 82°, between the constellations Taurus and Gemini. 
When it has moved 90° farther, to longitude 172°, in the con- 
stellation Leo, the edge of the ring is again turned towards 
the earth and sun. 

Thus there are a pair of opposite points of the orbit of Sat- 
urn in which the rings are turned edgewise to us, and another 
pair half-way between the first in which the ring is seen at 
its maximum inclination of about 27°. Since the planet per- 
forms a revolution in 29J years, these phases occur at average 



THE RINGS OF SATURN, 353 

intervals of about seven years and four months. The follow- 
ing are some of the times of their occurrence : 

1870. The planet being between Scorpio and Sagittarius, 
the ring was seen open to its greatest breadth, the north side 
being visible. The same phase recurs at the end of 1899. 

1878 (February 7th). The edge of the ring was turned tow- 
ards the sun, so that only a thin line of light was visible. The 
planet was then between Aquarius and Pisces. 

1885. The planet being in Taurus (the Bull) the south side 
of the rings will be seen at the greatest elevation. 

1892. The edge of the ring is again turned towards the sun, 
the planet being in Leo (the Lion). 

Owing to the motion of the earth, the times when the edge 
of the ring is turned towards it do not accurately correspond 
to those when it is turned towards the sun, and the points of 
Saturn's orbit in which this may occur range over a space of 
several degrees. The most interesting times for viewing the 
rings with powerful telescopes are on those rare occasions 
when the sun shines on one side of the ring, while the dark 
side is directed towards the earth. On these occasions the 
plane of the ring, if extended out far enough, would pass be- 
tween the sun and the earth. This was the case between Feb- 
ruary 9th and March 1st, 1878; but, unfortunately, at that time 
the earth and Saturn were on opposite sides of the sun, so that 
the planet was nearly lost in the sun's rays, and could be ob- 
served only low down in the west just after sunset. In 1891 
the position of Saturn will be almost equally unfavorable for 
the observation in question, as it can be made only in the early 
mornings of the latter part of October of that year, just after 
Saturn has risen. In fact, a good opportunity will not occur 
till 1907. In northern latitudes the finest telescopic views of 
Saturn and his ring may be obtained between 1881 and 1889, 
because during that interval Saturn passes his perihelion, and 
also the point of greatest northern declination, while the ring 
is opened out to its widest extent. In fact, these three most 
favorable conditions all fall nearly together during the years 
1881-'85. 



354 THE SOLAR SYSTEM. 

After Huyghens, the next step forward in discoveries on 
Saturn's ring was made by an English observer, named Ball, 
otherwise unknown in astronomy, who found that there were 
really two rings, divided by a narrow dark line. The breadth 
of the rings is very unequal, the inner ring being several times 
broader than the outer one. A moderate - sized telescope is 
sufficient to show this division near the extreme points of the 
ring if the atmosphere is steady ; but it requires both a large 
telescope and line seeing to trace it all the way across that 
part of the ring which is between the observer and the ball of 
the planet. Other divisions, especially in the outer ring, have 
at times been suspected by various observers, but if they real- 
ly existed, they must have been only temporary, forming and 
closing up again. 

In December, 1850, the astronomical world was surprised 
by the announcement that Professor Bond, of Cambridge, had 
discovered a third ring to Saturn. It lay between the rings 
already known and the planet, being joined to the inner edge 
of the inner ring. It had the appearance of a ring of crape, 
being so dark and obscure that it might easily have been 
overlooked in smaller telescopes. It was seen in England by 
Messrs. Lassell and Dawes before it was formally announced 
by the Bonds. Something of the kind had been seen by Dr. 
Galle, at Berlin, as far back as 1838 ; but the paper on the 
subject by Encke, the director of the observatory, did not de- 
scribe the appearance very clearly. Indeed, on examining the 
descriptions of observers in the early part of the eighteenth 
century, some reason is found for suspecting that they saw 
this dusky ring; but none of the descriptions are sufficiently 
definite to establish the fact, though it is strange if an object 
so plain as this ring now is should have been overlooked by 
all the older observers. 

The question whether changes of various sorts are going on 
in the rings of Saturn is one which is still unsettled. There 
is some reason to believe that the supposed additional divis- 
ions noticed in the rings from time to time are only errors of 
vision, due partly to the snading which is known to exist on 



THE EIXGS OF SATURX. 355 

various parts of the ring. By reference to the diagram of 
Saturn, it will be seen that the outer ring has a shaded line 
extending around it about two-thirds of the way from its in- 
ner to its outer edge. This line, however, is not fine and 
sharp, like the known division, but seems to shade off gradual- 
ly towards each edge. As observers who have supposed them- 
selves to see a division in this ring saw it where this shaded 
line is, and do not speak of the latter as anything distinct 
from the former, there is reason to believe that they mistook 
this permanent shading for a new division. The inner ring is 
brightest near its outer edge, and shades off gradually towards 
its inner edge. Here the dusky ring joins itself to it, and ex- 
tends about half-way in to the planet. 

As seen with the great Washington equatorial in the au- 
tumn of 1874, there was no great or sudden contrast be- 
tween the inner or dark edge of the bright ring and the out- 
er edge of the dusky ring. There was some suspicion that 
the one shaded into the other by insensible gradations. No 
one could for a moment suppose, as some observers have, that 
there was a separation between these two rings. All these 
considerations give rise to the question whether the dusky 
ring may not be growing at the expense of the inner bright 
ring. 

A most startling theory of changes in the rings of Saturn 
was propounded by Struve, in 1851. This was nothing less 
than that the inner edge of the ring was gradually approach- 
ing the planet in consequence of the whole ring spreading in- 
wards, and the central opening thus becoming smaller. The 
data on which this theory was founded were the descriptions 
and drawings of the rings by the astronomers of the seven- 
teenth century, especially Huyghens, and the measures ex- 
ecuted by later astronomers up to the time at which Struve 
wrote. The rate at which the space between the ring and the 
planet was diminishing seemed to be about 1".3 per century. 
The following are the numbers used by Struve, which are de- 
duced from the descriptions by the ancient observers, and the 
measures by the modern ones : 



356 



THE SOLAR SYSTEM. 





Year. 


Distance between 
Ring and Planet. 


Breadth of 
Ring. 


Huyghens 


1657 
1695 
1719 
1799 
1826 
1838 
1851 


6.5 

6.0 

5.4 

5.12 

4.36 

4.04 

3.67 


4.6 
5.1 

5.7 

5.98 

6.74 

7.06 

7.43 


Huyghens and Cassini 

Bradley. J 


Herschel 


W. Struve 


Encke and Galle 


Otto Struve 



If these estimates and measures were certainly accurate, 
they would place the fact of a progressive approach of the 
rings to the ball beyond doubt, an approach which, if it con- 
tinued at the same rate, would bring the inner edge of the 
ring into contact with the planet about the year 2150. But 
in measuring such an object as the inner edge of the ring of 
Saturn, which, as we have just said, seems to fade gradually 
into the obscure ring, different observers will always obtain 
different results, and the differences among the four observ- 
ers commencing "with W. Struve are no greater than are often 
seen in measuring an object of such uncertain outline. Hence, 
considering the great improbability of so stupendous a cosmi- 
cal change going on with so much rapidity, Struve's theory has 
always been viewed with doubt by other astronomers. 

At the same time, it is impossible to reconcile the descrip- 
tions by the early observers with the obvious aspect of the 
ring as seen now without supposing some change of the kind. 
The most casual observer who now looks at Saturn will see 
that the breadth of the two bright rings together is at least 
half as great again, if not twice as great, as that of the dark 
space between the inner edge of the bright ring and the plan- 
et. But Huyghens describes the dark space as about equal 
to the breadth of the ring, or a little greater. Supposing the 
ring the same then as now, could this error have arisen from 
the imperfection of his telescope % No ; because the effect of 
the imperfection would have been directly the opposite. The 
old telescopes all represented planets and other bright objects 
too large, and therefore would show dark spaces too small, 
owing to the irradiation produced by their imperfect glasses. 
A strong confirmation of Struve's view is found in the old 



CONSTITUTION OF THE RING. 357 

pictures given in Fig. 89 by those observers who could not 
clearly make out the ring. In nearly all cases the dark spaces 
were more conspicuous than the edges of the ring. But if 
we now look at Saturn through a very bad atmosphere, though 
the elliptical outline of the ring may be clearly made out, 
the dark space will be almost obliterated by the encroachment 
of the light of the planet and ring upon it. The question is, 
therefore, one of those the complete solution of which must 
be left to future observers. 

§ 5. Constitution of the Ring. 

The difficulties which investigators have met with in ac- 
counting for the rings of Saturn are of the same nature as 
those we have described as arising from spectroscopic discov- 
eries respecting the envelopes of the sun. They illustrate the 
philosophic maxim that surprise — in which term we may in- 
clude all difficulty and perplexity which men meet with in 
seeking to account for the phenomena of nature — is a result 
of partial knowledge, and cannot exist either with entire ig- 
norance or complete knowledge. Those who are perfectly 
ignorant are surprised at nothing, because they expect noth- 
ing, while perfect knowledge of what is to happen also pre- 
cludes the same feeling. The astronomers of two centuries 
ago saw nothing surprising in the fact of a pair of rings sur- 
rounding a planet, and accompanying it in its orbit, because 
they were not acquainted with the effects of gravitation on 
such bodies as the rings seemed to be. But when Laplace in- 
vestigated the subject, he found that a homogeneous and 
uniform ring surrounding a planet could not be in a state 
of stable equilibrium. Let it be balanced ever so nicely, the 
slightest external force, the attraction of a satellite or of a 
distant planet, would destroy the equilibrium, and the ring 
would soon be precipitated upon the planet. He therefore 
remarked that the rings must have irregularities in their 
form, such as Herschel supposed he had seen; but he did 
not investigate the question whether with those irregularities 
the equilibrium would really be stable. 



358 TEE SOLAR SYSTEM. 

The question was next taken up in this country by Profess- 
ors Peirce and Bond. The latter started from the supposed 
result of observations — that new divisions show themselves 
from time to time in the ring, and then close up again. He 
thence inferred that the rings must be fluid, and, to confirm 
this view, he showed the impossibility of even an irregular 
solid pair of rings fulfilling all the necessary conditions of 
stability and freedom of motion. Professor Peirce, taking up 
the same subject from a mathematical point of view, found 
that no conceivable form of irregular solid ring would be in a 
state of stable equilibrium; he therefore adopted Bond's view 
that the rings were fluid. Following up the investigation, 
he found that even a fluid ring would not be entirely stable 
without some external support, and he attributed that support 
to the attractions of the satellites. But as Laplace did not 
demonstrate that irregularities would make the ring stable, so 
Peirce merely fell back upon the attraction of the satellites as 
a sort of forlorn hope, but did not demonstrate that the fluid 
ring would really be stable under the influence of their attrac- 
tion. Indeed, it now seems very doubtful whether this at- 
traction would have the effect supposed by Peirce. 

The next, and, we may say, the last, important step was 
taken by Professor J. Clerk Maxwell, of England, in the 
Adams prize essay for 1856. He brought forward objections 
which seem unanswerable against both the solid and the fluid 
ring, and revived a theory propounded by Cassini about the 
beginning of the last century.* This astronomer considered 
the ring to be formed by a cloud of satellites, too small to 
be separately seen in the telescope, and too close together to 
admit of the intervals between them being visible. This is 
the view of the constitution of .the rings of Saturn now most 
generally adopted. The reason why the ring looks solid and 
continuous is that the satellites are too small and too numerous 
to be seen singly. They are like the separate little drops of 



* See Memoirs of the French Academy of Sciences for 1715, p. 47 ; or Cas- 
sini's "Fwle'mens d'Astronomie,"p. 338, Paris, 1740. 



THE SATELLITES OF SATURN. So ( J 

water of which clouds and fog are composed, which, to our 

eyes, seem like solid masses. In the dusky ring the particles 
may be so scattered that we can see through the cloud, the 
reason that it looks dusky being simply the comparatively 
small number of the particles, so that to the distant eye they 
appear like the faint stippling of an engraving. 

The question arises whether the comparative darknes 
some portions of the bright ring may not be due to the paucity 
of the particles, which allows the dark background of the sky 
to be seen through. This question cannot be positively an- 
swered until further observations are made ; but the prepon- 
derance of evidence favors the view that the entire bright 
ring is opaque, and that the dark shading is due entirely t<> a 
darker color of that part of the ring. Indeed, for anything 
we certainly know, the whole ring may be continuous and 
opaque, the darker shade of some parts arising solely from the 
particles being there black in color. The only way to settle 
conclusively the questions whether these parts of the ring louk 
black, owing to the sky beyond showing through opening.-, as 
it were, or from a black color of the' ring, is to find whether a 
stai» or other object can be seen through the dark spaces. But 
an opportunity for seeing a bright star through the ring has 
never yet presented itself. The most obvious way of settling 
the question in respect to the dusky ring is to notice whether 
the planet itself can be seen through it ; but this is much more 
difficult than might be supposed, owing to the ill -defined as- 
pect of the ring. The testimony of both Lassell and Trouve- 
lot is in favor of the view that this ring is partially transpar- 
ent ; but their observations will need to be repeated when the 
ring is opened out to our sight after 1882. 

§ 6. The Satellites of Saturn. 

When Huyghens commenced his observations of Saturn in 
1655, he saw a star near the planet which a few days' observa- 
tion enabled him to recognize as a satellite revolving round it 
in about fifteen days. In his rt Systema Saturnium," he vent- 
ured to express the opinion that this discovery completed the 



360 



THE SOLAR SYSTEM. 



solar system, which now comprised six planets (Saturn being 
then the outermost known planet) and six satellites (one of 
the earth, four of Jupiter, and this one of Saturn), making 
the perfect number of twelve. He was, therefore, confident 
that no more satellites were left to discover, and through fail- 
ing to search for others, he probably lost the honor of addi- 
tional discoveries. 

Twelve years after this prediction, Cassini discovered a sec- 
ond satellite outside that found by Huyghens, and within a 
few years more he found three others inside of it. The dis- 
covery of four satellites by one astronomer was so brilliant a 
result of French science that the Government of France 
struck a medal in commemoration of it, bearing the inscrip- 
tion Saturni Satellites primum cogniti. These ~Rve satellites 
completed the number known for more than a century. In 
1789 Herschel discovered two new ones still nearer the ring 
than those found by Cassini. The space between the ring and 
the inner one is so small that the satellite is generally invisible, 
even in the most powerful telescopes. Finally, in September, 
1848, the Messrs. Bond, at the Observatory of Harvard Col- 
lege, found an eighth satellite, while examining the ring of 
Saturn. By a singular coincidence, this satellite was found by 
Mr. Lassell, of England, only a couple of nights after it was 
detected by the Bonds. The names which have been given to 
these bodies are shown in the following list, in which the sat- 
ellites are arranged in the order of their distance from the 
planet. The distances are given in semidiameters of Saturn. 
More exact elements will be found in the Appendix to this 
volume. 



No. 


Name. 


Distance from 
Planet. 


Discoverer. 


Date. 


1 

2 
3 
4 

5 
6 

7 
8 


Mimas 

Enceladus. 

Tethys 

Dione 

Rhea 

Titan 

Hyperion . 
Japetus.... 


3.3 

4.3 

5.3 

6.8 

9.5 

20.7 

26.8 

64.4 


Herschel. . 
Herschel. . 

Cassini 

Cassini — 

Cassini 

Huyghens. 

Bond 

Cassini — 


1789, September 17th. 
1789, August 28th. 
1684, March. 
1684, March. 
1672, December 23d. 
1655, March 25th. 
1848, September 16th. 
1671, October. 



URANUS AND ITS SATELLITES. 361 

The brightness, or rather, the visibility, of these satellites 
follows the same order as their discovery. The smallest tel- 
escope will show Titan, and one of very moderate size will 
show Japetus in the western part of its orbit. Four or five 
inches aperture will show Bhea, and perhaps Tethys and Di- 
one, while seven or eight inches are required for Enceladus, 
and even with that aperture it will probably be seen only near 
its greatest elongation from the planet. Mimas can be seen 
only near the same position, unless the ring is seen edgewise, 
and will then require a large telescope, probably twelve inches 
or upwards. Finally, Hyperion can be recognized only with 
the most powerful telescopes, not only on account of its faint- 
ness, but of the difficulty of distinguishing it from minute stars. 

All these satellites, except Japetus, revolve \ery nearly in 
the plane of the ring. Consequently, when the edge of the 
ring is turned towards the earth, the satellites seem to swing 
from one side of the planet to the other in a straight line, run- 
ning along the thin edge of the ring, like beads on a string. 
This phase affords the best opportunity of seeing the inner 
satellites Mimas and Enceladus, because they are no longer 
obscured by the brilliancy of the ring. 

Japetus, the outer satellite of all, exhibits this remarkable 
peculiarity, that while in one part of its orbit it is the bright- 
est of the satellites, except Titan, in the opposite part it is al- 
most as faint as Hyperion, and can be seen only in large 
telescopes. When west of the planet, it is bright ; when east 
of it, faint. This peculiarity has been accounted for only by 
supposing that the satellite, like our moon, always presents 
the same face to the planet, and that one side of it is white 
and the other intensely black. The only difficulty in the way 
of this explanation is that it is doubtful whether any known 
substance is so black as one side of the satellite must be to 
account for such great changes of brilliancy. 

§ 7. Uranus and its Satellites. 

Uranus, the next planet beyond Saturn, is at a mean dis- 
tance from the sun of about 1770 millions of miles, and per- 



362 THE SOLAR SYSTEM. 

forms a revolution in 84 years. It shines as a star of the sixth 
magnitude, and can therefore be seen with the naked eye, if 
one knows exactly where to look for it. It was in opposition 
February 11th, 1877, and the time of opposition during the 
remainder of the present century may be found by adding 4^- 
days for every year subsequent to 1877. To find it readily, 
either with a telescope or the naked eye, recourse must be had 
to the Nautical Almanac, where the position (right ascension 
and declination) is given for each day in the year. 

Of course the smallest telescopes will show this planet as a 
star, but to recognize its disk a magnifying power of at least 
100 should be used, and 200 will be necessary to any one who 
is not a practised observer. As seen in a large telescope, the 
planet has a decided sea-green color. No markings have ever 
been certainly seen on the disk, and therefore no changes 
which could be due to an axial rotation have ever been estab- 
lished ; but it may be regarded as certain that it does rotate 
in the same plane in which the satellites revolve around it. 

Discovery of Uranus. — This planet was discovered by Sir 
William Herschel, in March, 1781. Perceiving by its disk 
that it was not a star, and by its motion that it was not a neb- 
ula, he took it for a comet. The possibility of its being a new 
planet did not at first occur to him ; and he therefore com- 
municated his discovery to the Royal Society as being one of 
a new comet. Various computing astronomers thereupon at- 
tempted to find the orbit of the supposed comet, from the ob- 
servations of Herschel an4 others, assuming it to move in a 
parabola, like other comets. But the actual motion of the 
body constantly deviated from the orbits thus computed to 
such an extent that new calculations had to be repeatedly 
made. After a few weeks it was found that if it moved in a 
parabola, the nearest distance to the sun must be at least four- 
teen times that of the earth from the sun, a perihelion distance 
many times greater than that of any known comet. This an- 
nouncement gave the hint that some other hypothesis must be 
resorted to, and it was then found that all the observations 
could be well represented by a circular orbit, with a radius 



URANUS AND ITS SATELLITES. 303 

nineteen times that of the earth's orbit. The object was, there- 
fore, a planet moving at double the distance of Saturn. 

With a commendable feeling of gratitude towards the royal 
patron who had afforded him the means of making his dis- 
coveries, Ilerschel proposed to call the new planet Georgium 
Sidus (the Star of the Georges). This name, contracted to " the 
Georgian," was employed in England until 1850, but never 
came into use on the Continent. Lalande thought the most 
appropriate name of the planet was that of its discoverer, and 
therefore proposed to call it Ilerschel. But this name met 
with no more favor than the other. Several other names were 
proposed, but that of Uranus at length met with universal 
adoption. It was proposed by Bode as the most appropriate, 
on the ground that the most distant body of our system might 
be properly named after the oldest of the gods. 

After the elliptic orbit of the planet had been accurately 
computed, and its path mapped out in the heavens, it was 
found that it had been seen a surprising number of times as a 
star without the observers having entertained any suspicion of 
its planetary nature. It had passed through the field of their 
telescopes, and they had noted the time of its transit, or its 
declination, or both, but had entered it in their journals simply 
as an unnamed star of the constellation in which it happened 
to be at the time. It had been thus seen five times by Flam- 
steed, the first observation being in 1690, nearly a century be- 
fore the discovery by Ilerschel. What is most extraordina- 
ry, it had been observed eight times in rapid succession by 
LeMonnier, of Paris, in December, 1768, and January, 1769. 
Had that astronomer merely taken the trouble to reduce and 
compare his observations, he would have anticipated Herschel 
by twelve years. Indeed, considering how easily the planet 
can be seen with the naked eye, it is illustrative of the small 
amount of care devoted to cataloguing the stars that it was 
not discovered without a telescope. 

Satellites of Uranus. — In January and February, 1.787, 
Herschel found that Uranus was accompanied by two satel- 
lites, of which the inner performed a revolution in a little less 



364 THE SOLAR SYSTEM. 

than nine days, and the outer in thirteen days and a half. 
The existence of these two satellites was well authenticated 
by his observations, and they have been frequently observed 
in recent times. They can be seen with a telescope of one- 
foot aperture or upwards. Afterwards Herschel made a very 
assiduous search for other satellites. He encountered many 
difficulties, not only from the extreme faintness of the objects, 
but from the difficulty of deciding whether any object he 
might see was a satellite, or a small star which happened to 
be in the neighborhood. He at length announced the probable 
existence of four additional satellites, the orbit of one being 
inside of those of the two certain ones, one between them, and 
two outside them. This made an entire number of six; and 
though the evidence adduced by Herschel in favor of the ex- 
istence of the four additional ones was entirely insufficient, 
and their existence has been completely disproved, they figure 
in some of our books on astronomy to this day. 

For half a century no telescope more powerful than that of 
Herschel was turned upon Uranus, and no additional light was 
thrown upon the question of the existence or non-existence of 
the questionable objects. At length, about 1846, Mr. William 
Lassell, of England, constructed a reflector of two feet aper- 
ture, of which we have already spoken, and of very excellent 
definition, which in optical power exceeded any of the older 
instruments. With this he succeeded in discovering two new 
satellites inside the orbits of the two brighter ones,* but found 
no trace of any of the additional satellites of Herschel. In the 
climate of England, he could make only very imperfect obser- 
vations of these bodies ; but in 1852 he moved his telescope 
temporarily to Malta, to take advantage of the purer sky of 
that latitude, and there he succeeded in determining their or- 
bits with considerable accuracy. Their times of revolution 
are about 2-J- and 4 days respectively. They may fairly be 

* These difficult objects were also sought for by Otto Struve with the fifteen- 
inch telescope of the Pulkowa Observatory, and occasional glimpses of them were, 
he believed, attained before they were certainly found by Mr. Lassell, but he was 
not able to follow them so continuously as to fix upon their times of revolution. 



VRANUS AND ITS SATELLITES. 365 

regarded as the most difficult known objects in the planetary 
system; indeed, it is only with a few of the most powerful 
telescopes in existence that they have certainly been seen. 

The non-existence of Ilerschel's suspected satellites is proved 
by the fact that they have been sought for in vain, both with 
Mr. LasselPs great reflectors and with the Washington twen- 
ty-six-inch refractor, all of which are optically more powerful 
than the telescopes of Ilerschel. There may be additional 
satellites which have not yet been discovered ; but if so, they 
must be too faint to have been recognized by Ilerschel. Pro- 
fessor Ilolden, of the Naval Observatory, has sought to show- 
that some of Ilerschel's observations of his supposed inner sat- 
ellites were really glimpses of the objects afterwards discov- 
ered by Mr. Lassell. This he has done by calculating the po- 
sitions of these inner satellites from tables for the date of 
each of Ilerschel's observations, and comparing them with the 
position of the object noted by Ilerschel. In four cases, the 
agreement is sufficiently close to warrant the belief that Iler- 
schel actually saw the real satellites; but Mr. Lassell attributes 
these coincidences to chance, and contests Professor Holden's 
views. 

The most remarkable peculiarity of the satellites of Uranus 
is the great inclination of their orbits to the ecliptic. Instead 
of being inclined to it at small angles, like the orbits of all 
the other planets and satellites, they are nearly perpendicular 
to it ; indeed, in a geometrical sense, they are more than per- 
pendicular, because the direction of the motion of the satel- 
lites in their orbits is retrograde. To change the position of 
the orbit of an ordinary satellite into that of the orbits of 
these satellites, it would have to be tipped over 100° ; so that, 
supposing the orbit a horizontal plane, the point correspond- 
ing to the zenith would be 10° below the horizon, and the up- 
per surface would be inclined beyond the perpendicular, so as 
to be the lower of the two surfaces. 

Observations of the satellites afford the only accurate way 
of determining the mass of Uranus ; because, of the adjoining 
planets, Saturn and Neptune, the observations of the first are 



3G6 THE SOLAR SYSTEM. 

too uncertain and those of the last too recent to give any cer- 
tain result. Measures made with the great Washington tele- 
scope show this mass to be whnr > a result which is probably 
correct within -^-J-g- part of its whole amount.* 

§ 8. Neptune and its Satellite. 

The discovery of this planet is due to one of the boldest and 
most brilliant conceptions of modern astronomy. The planet 
was felt, as it were, by its attraction upon Uranus; and its di- 
rection was thus calculated by the theory of gravitation before 
it had been recognized by the telescope. An observer was 
told that if he pointed his telescope towards a certain point in 
the heavens, he would see a new planet. He looked, and there - 
was the planet, within a degree of the calculated place. It is 
difficult to imagine a more striking illustration of the certain- 
ty of that branch of astronomy which treats of the motions of 
the heavenly bodies and is founded on the theory of gravi- 
tation. 

To describe the researches which led to this result, we shall 
have to go back to 1820. In that year, Bouvard, of Paris, 
prepared improved tables of Jupiter, Saturn, and Uranus, 
which, although now very imperfect; have formed the basis of 
most of the calculations since made on the motions of those 
bodies. He found that while the motions of Jupiter and Sat- 
urn were fairly in accord with the theory of gravitation, it 
w r as not so with those of Uranus. After allowing for the per- 
turbations produced by the known planets, it was impossible 
to find any orbit which would satisfy both the ancient and the 
recent observations of Uranus. By the ancient observations 
we mean those accidental ones made by Flamsteed, Le Mon- 
nier, and others, before the planetary character of the object 
was suspected ; and by the recent ones, those made after the 
discovery of the planet by Herschel, in 1781. Bouvard, there- 
fore, rejected the older observations, founding his tables on the 
modern ones alone; and leaving to future investigators the 

* Washington Observations for 1873 : Appendix. 



NEPTUNE AND ITS SATELLITE. 307 

question whether the difficulty of reconciling the two systems 
arose from the inaccuracy of the ancient observations, or from 
the action of some extraneous influence upon the planet. 

Only a few years elapsed, when the planet began to deviate 
from the tables of Bouvard. In 1830 the error amounted to 
20"; in 1840, to 90"; in 1844, to 2'. From a non- astro- 
nomical point of view, these deviations were very minute. 
Had two stars moved in the heavens, the one in the place 
of the real planet, the other in that of the calculated planet, 
it would have been an eye of wonderful keenness which 
could have distinguished the two from a single star, even in 
1844. But, magnified by the telescope, it is a large and 
easily measurable quantity, not for a moment to be neglect- 
ed. The probable cause of the deviation was sometimes a 
subject of discussion among astronomers, but no very definite 
views respecting it seem to have been entertained, nor did 
any one express the decided opinion that it was to be attrib- 
uted to a trans-Uranian planet, natural as it seems to us such 
an opinion would have been. 

In 1845, Arago advised his then young and unknown friend 
Leverrier, whom he knew to be an able mathematician and 
an expert computer, to investigate the subject of the motions 
of Uranus. Leverrier at once set about the task in the most 
systematic manner. The first step was to make sure that the 
deviations did not arise from errors in Bouvard's theory and 
tables ; he therefore commenced with a careful recomputation 
of the perturbations of Uranus produced by Jupiter and Sat- 
urn, and a critical examination of the tables. The result was 
the discovery of many small errors in the tables, which, how- 
ever, were not of a character to give rise to the observed de- 
viations. 

The next question was whether any orbit could be assigned 
which, after making allowance for the action of Jupiter and 
Saturn, would represent the modern observations. The an- 
swer was in the negative, the best orbit deviating, first on one 
side and then on the other, by amounts too great to be attrib- 
uted to errors of observation. Supposing the deviations to be 

25 



368 THE SOLAR SYSTEM. 

due to the attraction of some unknown planet, Leverrier next 
inquired where this planet must be situated. Its prbit could 
not lie between those of Saturn and Uranus, because then it 
would disturb the motions of Saturn as well as those of Uranus. 
Outside of Uranus, therefore, the planet must be looked for, 
and probably at not far from double the distance of that 
body ; this being the distance indicated by the law of Titius. 
Complete elements of the orbit of the unseen planet were 
finally deduced, making its longitude 325° as seen from the 
earth at the beginning of 1847. This conclusion was reached 
in the summer of 1846. 

Leverrier was not alone in reaching this result. In 1843, 
Mr. John C. Adams, then a student at Cambridge University, 
England, having learned of the discordances in the theory of 
Uranus from a report of Professor Airy, attacked the same 
problem which Leverrier took hold of two years later. In 
October, 1845, he communicated to Professor Airy elements 
of the planet so near the truth that, if a search had been made 
with a large telescope in the direction indicated, the planet 
could hardly have failed to be found. The Astronomer Royal 
was, however, somewhat incredulous, and deferred his search 
for further explanations from Mr. Adams, which, from some 
unexplained cause, he did not receive. Meanwhile the planet, 
which had been in opposition about the middle of August, 
was lost in the rays of the sun, and could not be seen before 
the following summer. A most extraordinary circumstance 
was that nothing was immediately published on the subject of 
Mr. Adams's labors, and no effort made to secure his right to 
priority, although in reality his researches preceded those of 
Leverrier by nearly a year. 

In the summer of 1846, M. Leverrier's elements appeared, 
and the coincidence of his results with those of Mr. Adams 
was so striking, that Professor Challis, of the Cambridge Ob- 
servatory, commenced a vigorous search for the planet. Un- 
fortunately, he adopted a mode of search which, although it 
made the discovery of the planet certain, was extremely la- 
borious. Instead of endeavoring to recognize it by its disk, 



NEPTUNE AND ITS SATELLITE. 369 

lie sought to detect it by its motion among the stars — a 
course which required all the stars in the neighborhood to 
have their positions repeatedly determined, so as to find 
which of them had changed its position. Observations of 
the planet as a star were actually made on August 4-th. 1846, 
and again on August 12th ; but these observations, owing to 
Mr. Challis's other engagements, were not reduced, and so the 
fact that the planet was observed did not appear. His mode 
of proceeding was much like that of a man who. knowing that 
a diamond had dropped near a certain spot on the sea-beach, 
should remove all the sand in the neighborhood to a conven- 
ient place for the purpose of sifting it at his leisure, and 
should thus have the diamond actually in his possession with- 
out being able to recognize it. 

Early in September, 1846, while Professor Challis was still 
working away at his observations, entirely unconscious that 
the great object of search was securely imprisoned in the pen- 
cilled figures of his note-book, Leverrier wrote to Dr. Galle. at 
Berlin, suggesting that he should try to find the planet. It 
happened that a map of the stars in the region occupied by 
the planet was just completed, and on pointing the telescope 
of the Berlin Observatory, Galle soon found an object which 
had a planetary disk, and was not on the star map. Its posi- 
tion was carefully determined, and on the night following it 
was re-examined, and found to have changed its place among 
the stars. No further doubt could exist that the lonjj-soueht- 
for planet was found. The date of the optical discovery was 
September 23d, 1846. The news reached Professor Challis 
October 1st, and, looking into his note-book, he found his own 
observations of the planet, made nearly two months before. 

As between Leverrier and Adams, the technical right of 
priority in this wonderful investigation lay with Leverrier, al- 
though Adams had preceded him by nearly a year, for the 
double reason that the latter did not publish his results before 
the discovery of the planet, and that it was by the directions 
of Leverrier to Dr. Galle that the actual discovery was made. 
But this does not diminish the credit due to Mr. Adams for 



370 THE SOLAR SYSTEM. 

his boldness in attacking, and his skill in successfully solving, 
so noble a problem. The spirit of true science is advancing 
to a stage in which contests about priority are looked upon as 
below its dignity. Discoveries are made for the benefit of 
mankind ; and if made independently by several persons, it is 
fitting that each should receive all the credit due to success in 
making it. We should consider Mr. Adams as entitled to the 
same unqualified admiration which is due to a sole discoverer; 
and whatever claims to priority he may have lost by the more 
fortunate Leverrier will be compensated by the sympathy 
which must ever be felt towards the talented young student 
in his failure to secure for his work that immediate publicity 
which was due to its interest and importance. 

The discovery of Neptune gave rise to a series of research- 
es, in which American astronomers took a distinguished part. 
One of the first questions to be considered was whether the 
planet had, like Uranus, been observed as a star by some pre- 
vious astronomer. This question was taken up by Mr. Sears 0. 
Walker, of the Naval Observatory. A few months' observa- 
tion sufficed to show that the distance of the planet from the 
sun was not far from 30 (the distance of the earth being, as 
usual, unity), and, assuming a circular orbit, he computed the 
approximate place of the planet in past years. He traced its 
course back from year to year in order to find whether at any 
time it passed through a region which was at the same time 
being swept by the telescopes of observers engaged in prepar- 
ing catalogues of stars. He was not successful till he reached 
the year 1795. On the 8th and 10th of May of that year, 
Lalande, of Paris, had swept over the place of the planet. It 
must now be decided whether any of the stars observed on 
those nights could have been Neptune. Although the exact 
place of the planet could not yet be fixed for an epoch so 
remote, it was easy to mark out the apparent position of its 
orbit as a line among the stars, and it must then have been 
somewhere on that line. After taking out the stars which 
were too far from the line, and those which had been seen by 
subsequent observers, there remained one, observed on May 



NEPTUNE AND ITS SATELLITE. 371 

10th, which was very near the computed orbit. Walker at 
once ventured on the bold prediction that if this region of 
the heavens were examined with a telescope, thai star would 
be found missing. He communicated this opinion officially 
to Lieutenant Maury and other scientific men in Washington, 
and asked that the search might be made. On the first clear 
evening the examination was made by Professor Hubbard, 
and, surely enough, the star was not there. 

There was, however, one weak point in the conclusion that 
this was really the planet Neptune. Lalande had marked his 
observation of the missing star with a colon, to indicate that 
there was a doubt of its accuracy : therefore it was possible 
that the record of the supposed star might have been the sim- 
ple result of some error of observation. Happily, the original 
manuscripts of Lalande were carefully preserved at the Paris 
Observatory ; and as soon as the news of Walker's researches 
reached that city an examination of the observations of May 
8th and 10th, 1795, was entered upon. The extraordinary dis- 
covery was made that there was no mark of uncertainty in the 
original record, but that Lalande had observed the planet both 
on the Sth and 10th of May. The object having moved slight- 
ly during the two days' interval, the observations did not 
agree ; and Lalande supposed that one of them must be wrong, 
entirely unconscious that in that little discrepancy lay a dis- 
covery which would have made his name immortal. "Without 
further examination, he had rejected the first observation, and 
copied the second as doubtful on account of the discrepancy, 
and thus the pearl of great price was dropped, not to be 
found again till a half-century had elapsed. 

For several years the investigation of the motion of the new 
planet was left in the hands of Mr. Walker and Professor 
Peirce. The latter was the first one to compute the perturba- 
tions of Neptune produced by the action of the other planets. 
The results of these computations, together with Mr. Walk- 
er's elements, are given in the Proceedings of the American 
Academy of Arts and Sciences. 

Physical Aspect of Xej)tune. — On the physical appearance of 






372 THE SOLAR SYSTEM. 

this planet very little can be said. In the largest telescopes 
and through the finest atmosphere, it presents the appearance 
of a perfectly round disk about 3" in diameter, of a pale-blue 
color. No markings have been seen upon it. When first 
seen by Mr. Lassell, he suspected a ring, or some such append- 
age ; but future observations under more favorable circum- 
stances showed this suspicion to be without foundation. To 
recognize the disk of Neptune with ease, a magnifying power 
of 300 or upwards must be employed. 

Satellite of Neptune. — Soon after the discovery of Neptune, 
Mr. Lassell, scrutinizing it with his two-foot reflector, saw on 
various occasions a point of light in the neighborhood. Dur- 
ing the following year it proved to be a satellite, having a pe- 
riod of revolution of about 5 days 21 hours. During 1347 
and 1848 the satellite was observed, both at Cambridge by the 
Messrs. Bond, and at Pulkowa by Strnve. These observations 
showed that its orbit was inclined about 30° to the ecliptic, 
but it was impossible to decide in which direction it was mov- 
ing, since there were two positions of the orbit, and two di- 
rections of motion, in which the apparent motion, as seen from 
the earth, would be the same. After a few years the change 
in the direction of the planet enabled this question to be de- 
cided, and showed that the motion was retrograde. The ease 
was more extraordinary than that of the satellites of Uranus, 
since, to represent both the position of the orbit and the di- 
rection of motion in the usual way, the orbit would have to be 
tipped over 150° ; it is, in fact, nearly upside down. The de- 
terminations of the elements of the satellite have been ex- 
tremely discordant, a circumstance which we must attribute 
to its extreme faintness. It is a minute object, even in the 
most powerful telescopes. 

Measures of the distance of the satellite from the planet, 
made with the great Washington telescope, show the mass of 
Neptune to be T9"3"w- The mass deduced from the perturba- 
tions of Uranus is Y $ \ 6 o ? an agreement as good as could be 
expected in a quantity so difficult to determine. 



ASPECTS AND FORMS OF COMETS. 373 



CHAPTER V. 

COMETS AND METEORS. 

§ 1. Aspects and Forms of Comets. 

The celestial motions which we have hitherto described 
take place with a majestic uniformity which has always im- 
pressed the minds of men with a sense of the unchangeable- 
ness of the heavens. But this uniformity is on some occasions 
broken by the apparition of objects of an extraordinary as- 
pect, which hover in the heavens for a few days or weeks, like 
some supernatural visitor, and then disappear. We refer to 
comets, bodies which have been known from the earliest times, 
but of which the nature is not yet deprived of mystery. 

Comets bright enough to be noticed with the naked eye 
consist of three parts, which, however, are not completely dis- 
tinct, but run into each otber by insensible degrees. These 
are the nucleus, the coma, and the tail. 

The nucleus is the bright centre which to the eye presents 
the appearance of an ordinary star or planet. It would hard- 
ly excite remark but for the coma and tail by which it is ac- 
companied. 

The coma (which is Latin for hair) is a mass of cloudy or 
vaporous appearance, which surrounds the nucleus on all sides. 
Next to the nucleus, it is so bright as to be hardly distinguish- 
able from it, but it gradually shades off in every direction. 
Nucleus and coma combined present the appearance of a star, 
more or less bright, shining through a small patch of fog, and 
are together called the head of the comet. 

The tail is a continuation of the coma, and consists of a 
stream of milky light, growing wider and fainter as it recedes 
from the comet, until the eye can no longer trace it. A curi- 



374: THE SOLAR SYSTEM. 

ous feature, noticed from the earliest times, is that the tail is 
always turned from the sun. The extent of the tail is very 
different in different comets, that appendage being brighter 
and longer the more brilliant the comet. Sometimes it might 
almost escape notice, while in many great comets recorded in 
history it has extended half-way across the heavens. The 
actual length, when one is seen at all, is nearly always many 
millions of miles. Sometimes, though rarely, the tail of the 
comet is split up into several branches, extending out in 
slightly different directions. 

Such is the general appearance of a comet visible to the 
naked eye. When the heavens were carefully swept with tel- 
escopes, it was found that comets thus visible formed but a 
small fraction of the whole number. If a diligent search is 
kept up, as many comets are sometimes found with the tele- 
scope in a single year as would be seen in a lifetime with the 
unaided eye. These " telescopic comets " do not always pre- 
sent the same aspect as those seen with the naked eye. The 
coma, or foggy light, generally seems to be developed at the 
expense of the nucleus and the tail. Sometimes either no 
nucleus at all can be seen with the telescope, or it is so faint 
and ill-defined as to be hardly distinguishable. In the cases 
of such comets, it is generally impossible to distinguish the 
coma from the tail, the latter being either entirely invisible, 
or only an elongation of the coma. Many well-known comets 
consist of hardly anything but a patch of foggy light of more 
or less irregular form. 

Notwithstanding these great apparent differences between 
the large comets and the telescopic ones, yet, when we close-' 
ly watch their respective modes of development, we find them 
all to belong to one class. The differences are like those be- 
tween some animals, which, to the ordinary looker-on, have 
nothing in common, but in which the zoologist sees that every 
part of the one has its counterpart in the other — indeed, the 
analogy between what the astronomer sees in the growth of 
comets and the zoologist in the growth of animals is quite 
worthy of remark. As a general rule, all comets look nearly 






ASPECTS AND FORMS OF COMETS. 



3T5 




Fig. DO.— Views oi Kucke's comet iu 1&71, by Dr. Vugel. 

alike when they first come within reach of the telescope, the 
subsequent diversities arising from the different developments 
of corresponding parts. The first appearance is that of a lit- 
tle foggy patch without any tail, and very often without any 
visible nucleus. Thus, in the case of Donati's comet of 1S58, 
one of the most splendid on record, it was more than two 
months after the first discovery before there was any appear- 



376 THE SOLAR SYSTEM. 

ance of a tail. To enable the reader to see the relation of 
this to a very diffused telescopic comet, we present a telescopic 
view of the head of this great comet when near its brightest, 
and three .drawings of Encke's comet, made by Dr. Yogel, in 
November and December, 1871. 

When the nucleus of a telescopic comet begins to show it- 
self, it is commonly on the side farthest from the sun. Sev- 
eral little branches will then be seen stretched out in the di- 
rection of the sun, so that it will appear as if the comet had 
a small fan-shaped tail directed towards the sun, instead of 
from it, as is usual. Thus, in the pictures of Encke's comet 
in Figs. 1 and 2, the sun is towards the left, and we see what 




Fig. 91.— Head of Donati's great comet of 1858, after Bond. 

looks like three little tails, the middle one pointed towards the 
sun. But if we look at the view of Donati's comet, Fig. 91, 
we see several little lines branching upwards from the centre 
of the head, and it is to these, and not to the tail, that the lit- 
tle tails in the figures of Encke's comet correspond. In fact, 
the general rule is that the heads of comets have a fan-shaped 
structure, the handle of the fan being in the nucleus, and the 
middle arm pointing towards the sun ; and it is this append- 
age which first shows itself. 

In the larger comets, this fan is surrounded by one or more 



MOTIONS, ORIGIN, AND NUMBER OF COMETS. 377 

semicircular arches, or envelopes, the inner one forming its 
curved border; but this arch does not show itself in very faint 
comets. The true tail of the comet, when it appears, is always 
directed from the sun, and therefore away from the fan. In 
Fig. 90, No. 3, a very faint true tail will be seen extending 
out towards the lower right-hand corner of the picture, which 
was opposite to the direction of the sun. On the other hand, 
though the branches turned towards the sun have disappears], 
the fan-like form can still be traced in the head. In Fijr. 91, 
the true tail is turned downwards : owing to the large scale of 
the picture, only the commencement of it can be seen. The 
central line of the tail, it will be remarked, is comparatively 
dark. This is very generally the case with bright comets. 

§ 2. Motions, Origin, and Number of Comets. 

When it was found by Kepler that all the planets moved 
around the sun in conic sections, and when Newton showed 
that this motion was the necessary result of the gravitation of 
the planets towards the sun, the question naturally arose wheth- 
er comets moved according to the same law. It was found by 
Newton that the comet of 1680 actually did move in such an 
orbit, but instead of being, like the planetary orbits, nearly 
circular, it was yevy eccentric, being to all appearance a pa- 
rabola. 

A parabola being one of the orbits which gravitation would 
cause to be described, it was thus made certain that comets 
gravitated towards the sun, like planets. It was, however, im- 
possible to say whether the orbit was really a parabola or a 
very elongated ellipse. The reason of this difficulty is that 
comets are visible in only a very small portion of their orbits, 
quite close to the sun, and in this portion the forms of a pa- 
rabola and of a very eccentric ellipse are so nearly the same, 
that they cannot always be distinguished. 

There is this very important difference between an elliptical 
and a parabolic orbit — that the former is closed up, and a 
comet moving in it must come back some time, whereas the 
two branches of the latter extend out into infinite space with- 



378 



THE SOLAR SYSTEM. 



out ever meeting. 



A comet moving in a parabolic orbit will, 
therefore, never return, but, after once sweeping past the sun, 
will continue to recede into infinite space forever. The same 
thing will happen if the comet moves in an hyperbola, which is 



Parabolic orbit. Eccentric ellipse. 

Fig. 92.— Parabolic and elliptic orbit of a comet. The comet ie invisible in the dotted part 
of the orbits, and the forms of the visible parts, a, 6, cannot be distinguished in the 
two orbits. But the ellipse forms a closed curve, while the two branches of the pa- 
rabola continue forever without meeting. 

the third class of orbit that may be described under the influ- 
ence of gravitation. In a parabola, the slightest retardation 
of a comet would change the orbit into an ellipse, the velocity 
being barely sufficient to carry the comet off forever, whereas 
in an hyperbola there is more or less velocity to spare. Thus 
the parabola is a sort of dividing curve between the hyperbola 
and the ellipse. 

The astronomer, knowing the position of an orbit, can tell 
exactly what velocity is necessary at any point of it in order 
that a body moving in it may go off, never to return. A body 
thrown from the earth's surface with a velocity of seven miles 



MOTIONS, ORIGIN, AND NUMBER OF COMETS. 379 

a second, and not retarded by the atmosphere, would never 
return to the earth, but would describe some sort of an orbit 
round the sun. It would, in fact, be a little planet. If the 
earth were out of the way, a body moving past the earth's 
orbit at the rate of twenty -six miles a second would have just 
the velocity necessary to describe a parabola. If the velocity 
of a comet exceeds this limit at that point of its orbit which 
is 92J millions of miles from the sun, then the comet must 
go off into infinite space, never to return to our system. But 
with a less velocity the comet must be brought back by the 
sun's attraction at some future time, the time being longer the 
more nearly the velocity reaches twenty-six miles per second. 
It is by the velocity that the astronomer must, in general, de- 
termine the form of the orbit. If it corresponds exactly to 
the calculated limit, the orbit is a parabola ; if it exceeds this 
limit, it is an hyperbola ; if it falls short of it, it is an ellipse. 

Now, in the large majority of comets the velocity is so near 
the parabolic limit that it is not possible to decide, from ob- 
servations, whether it falls short of it or exceeds it. In the 
case of a few comets the observations indicate an excess of 
velocity, but an excess is so minute that its reality cannot be 
confidently asserted. It cannot, therefore, be said with cer- 
tainty that any known comet revolves in a hyperbolic orbit, 
and thus it is possible that all comets belong to our system, 
and will ultimately return to it. It is, however, certain that 
in the majority of cases the return will be delayed many cen- 
turies, nay, perhaps many thousand years. There are quite a 
number of comets which are known to be periodic, returning 
to the sun at regular intervals in elliptic orbits. Some of 
these have been observed at several returns, so that their exact 
period has been determined with great certainty : in the case 
of others, the periodicity has been inferred only from the fact 
that the velocity fell so far short of the parabolic limit that 
there could be no doubt of the fact that the comet moved in 
an ellipse. 

In this question of cometary orbits is involved the very in- 
teresting one, whether comets should be considered as belong- 



380 THE SOLAR SYSTEM. 

ing to our system, or as mere visitors from the stellar spaces. 
We may conceive of them as stray fragments of original neb- 
ulous matter scattered through the great wilderness of space 
around us, drawn towards our sun one by one as the long ages 
elapse. If no' planets surrounded the sun, or if, surrounding 
it, they were immovable, a comet thus drawn in would whirl 
around the sun in a parabolic orbit, and leave it again, not to 
return until millions of years had elapsed, because the veloci- 
ty it would acquire by falling towards the sun would be just 
sufficient to carry it back into the infinite void from which it 
came. But owing to the motions of the several planets in 
their orbits, the comet would have its velocity changed in 
passing each of thenij the change being an acceleration or a 
retardation, according to the way in which it passed. If the 
total accelerations produced by all the planets exceeded the 
retardations, the comet would leave our system with more 
than the parabolic velocity, and would certainly never return. 
If the retarding forces chanced to be in excess, the orbit 
would be changed into an ellipse more or less elongated, ac- 
cording to the amount of this excess. In the large majority 
of cases, the retardation would be so slight that the most del- 
icate observations could not show it, and it could be known 
only by calculation, or by the return of the comet after tens 
or hundreds of thousands of years. But should the comet 
chance to pass very near a planet, especially a large planet 
like Jupiter, the retardation might be so great as to make the 
comet revolve in an orbit of quite short period, and thus be- 
come a seemingly permanent member of our system. So near 
an approach of a comet to a planet would not be likely to oc- 
cur more than once in a number of centuries, but every time 
it did occur there would be an even chance for an additional 
comet of short period, the orbit of which would, at first, al- 
most intersect that of the planet which had deranged it. It 
might not, however, be a known comet, because the orbit 
might be wholly beyond the reach of our vision. 

It is impossible, in the present state of science, to say with 
certainty whether the periodic comets were thus brought into 



MOTIONS, ORIGIN, AND NUMBER OF COMETS. 381 

our system ; but it seems probable that they were, from the 
fact that many, if not all, of the orbits of these comets pa- 
near the orbits of some of the planets. That the planetary 
and cometary orbits in such a case should intersect now is not 
to be expected, because both would change by the secular 
variations resulting from the action of the planets. Future 
research will probably throw more light on this question. 

Number of Comets. — It was the opinion of Kepler that the 
celestial spaces were as full of comets as the sea of fish, only 
a small proportion of them coming within the range of our 
telescopes. That only an insignificant fraction of all existing 
comets have ever been observed, we may regard as certain. 
Owing to their extremely elongated orbits, they can be seen 
only when near their perihelion, and as it is probable that the 
period of revolution of the large majority of those which have 
been observed is counted by thousands' of years — if, indeed, 
they ever return at all — our observations must be continued 
for many thousand years before we have seen all which conic 
within range of our telescopes. It is also probable that all 
which can ever be seen will be but a small fraction of the 
number which exist, because a comet can seldom be seen un- 
less its perihelion is either inside the orbit of the earth, or but 
little outside of it. There are a few exceptions to the rule 
that only such comets are seen, the most notable one being 
that of the comet of 1729, which, at perihelion, was more than 
four times the earth's distance from the sun. This comet must 
have been one of extraordinary magnitude, as almost every 
other known comet would have disappeared entirely from the 
most powerful telescopes of that time, if placed at the dis- 
tance at which it was observed. 

The actual number of comets recorded as visible to the 
naked eye since the Christian era is given in the table on the 
following page.* 

* This table is taken at second-hand, principally from Arago ("Astronomie 
Populaire," livre xvii., chap. xv. ). Arago mentions but eight as visible during 
the eighteenth century. I have considered the number thirty-six, given by Klein, 
as more probable. 



3S2 



THE SOLAB SYSTEM. 



Years of our Era. 


Number 
of Comets. 


Years of our Era. 


Number 
of Comets. 


From to 100 


22 
23 
44 

27 
16 
25 
22 
16 
42 
26 


From 1001 to 1100 


36 
26 
26 
29 
27 
31 
12 
36 
16 


" 101 " 200 


" 1101 " 1200 


" 201 " 300 


" 1201 " 1300 


" 301 " 400 


" 1301 " 1400 


" 401 " 500 


" 1401 " 1500 


" 501 " 600 


" 1501 " 1600 


" 601 " 700 


" 1601 " 1700 


" 701 " 800 


" 1701 " 1800 


" 801 " 900 

" 901 " 1000 


" 1801 " 1875 







In round numbers, about five hundred comets visible to the 
naked eye have been recorded since our era, making a general 
average of one every four years. Besides these, nearly two 
hundred telescopic comets have been observed since the in- 
vention of the telescope ; so that the total number of these 
bodies observed during the period in question does not fall 
far short of seven hundred. Several new telescopic comets 
are now discovered nearly every year, the number sometimes 
ranging up to six or eight. It is probable that the annual 
number of this class discovered depends very largely on the 
skill, assiduity, and good - fortune of the astronomers who 
chance to be engaged in searching for them. 

§ 3. Remarkable Comets. 

In unenlightened ages comets were looked on with terror, 
as portending pestilence, war, the death of kings, or other 
calamitous or remarkable events. Hence it happens that in 
the earlier descriptions of these bodies, they are generally 
associated with some contemporaneous event. The descrip- 
tions of the comets themselves are, however, so vague and 
indefinite as to be entirely devoid of either instruction or in- 
terest, as it often happens that not even their course in the 
heavens is stated. 

The great comet of 1680 is, as already said, remarkable for 
being not only a brilliant comet, but the one by which New- 
ton proved that comets move under the influence of the gravi- 
tation of the sun. It first appeared in the autumn of 1680, 
and continued visible most of the time till the following spring. 



REMARKABLE COMETS. 383 

It fell down almost in a direct line to the sun, passing nearer 
to that luminary than any comet before known. It passed its 
perihelion on December 18th, and, sweeping round a large 
arc, went back in a direction not very different from that from 
which it came. The observations have been calculated and 
the orbit investigated by many astronomers, beginning with 
Newton ; but the results show no certain deviation from a 
parabolic orbit. Hence, if tl*e comet ever returns, it is only 
at very long intervals. Halley, however, suspected, witli some 
plausibility, that the period might be 575 years, from the fact 
that great comets had been recorded as appearing at that in- 
terval. The first of these appearances was in the month of 
September, after Julius Caesar was killed ; the second, in the 
year 531; the third, in February, 1106; while that of 1680 
made the fourth. If, as seems not impossible, these were four 
returns of one and the same comet, a fifth return will be seen 
by our posterity about the year 2255. Until that time the 
exact period must remain doubtful, because observations made 
two centuries ago do not possess the exactitude which will 
decide so delicate a point. 

Halley s Comet. — Two years after the comet last described, 
one appeared which has since become the most celebrated of 
modern times. It was first seen on August 19th, 1682, and 
observed about a month, when it disappeared. Halley com- 
puted the position of the orbit, and, comparing it with previ- 
ous orbits, found that it coincided so exactly with that of a 
comet observed by Kepler in 1607, that there could be no 
doubt of the identity of the two orbits. So close were they 
together that, if drawn on the heavens, the naked eye would 
almost see them joined into a single line. The chances against 
two separate comets moving in the same orbit were so great 
that Halley could not doubt that the comet of 16S2 was the 
same that had appeared in 1607, and that it therefore revolved 
in a very elliptic orbit, returning about every seventy-five years. 
His conclusion was confirmed by the fact that a comet was 
observed in 1531, which moved in apparently the same orbit. 
Again subtracting the period of seventv-five years, it was 

26 



384 THE SOLAR SYSTEM. 

found that the comet had appeared in 1456, when it spread 
such terror throughout Christendom that Pope Calixtus or- 
dered prayers to be offered for protection against the Turks 
and the comet. This is supposed to be the circumstance which 
gave rise to the popular myth of the Pope's Bull against the 
Comet. 

This is the earliest occasion on which observations of the 
course of the comet were made with such accuracy that its 
orbit could be determined. If we keep subtracting 75J years, 
we shall find that we sometimes fall on dates when the appa- 
rition of a comet was recorded; but without any knowledge 
of the orbits of these bodies, it cannot be said with certainty 
that they are identical. However, in the returns of 1456, 
1531, 1607, and 1682, at nearly equal intervals, Halley had 
good reason for predicting that the comet would return again 
about 1758. This gave the mathematicians time to investi- 
gate its motions; and the establishment, in the mean time, of 
the theory of gravitation showed them how to set about the 
work. It was necessary to calculate the effect of the attrac- 
tion of the planets on the motion of the comet during the en- 
tire seventy-six years. This immense labor was performed by 
Clairaut, who found that, in consequence of the attractions of 
Jupiter and Saturn, the return of the comet would be delayed 
618 days, so that it would not reach its perihelion until the 
middle of April, 1759. Not having time to finish his calcula- 
tions in the best way, he considered that this result was uncer- 
tain by one month. The comet actually did pass its perihelion 
at midnight on March 12th, 1759. 

Seventy-six years more were to elapse, and the comet would 
again appear about 1835. Meanwhile, great improvements 
were made in the methods of computing the effects of planet- 
ary attraction on the motions of a comet, so that mathemati- 
cians, without expending more labor than Clairaut did, were 
enabled to obtain much more accurate results. The French 
were still the leading nation of the world in this sort of inves- 
tigation, and the computation of the return of the comet was 
undertaken independently by two of their leading astronomers, 



REMARKABLE COMETS. 



:S5 



De Damoiseau and De Pontecoulant. Of these, the first an- 
nounced that it would reach its perihelion on November 4th, 
1835; while De Pontecoulant, after revising his computations 
with more exact determinations of the masses of the planets, 
assigned November 13th, at 2 a.m., as the date. The expected 
comet was, of course, looked for with the greatest assiduity, 
and was first seen on August 5th. Approaching the sun, it 
passed its perihelion on November 10th, at eleven o'clock in 
the morning, only three days after the time predicted by De 
Pontecoulant. 

This was the last return of the celebrated comet of Halley, 
It was followed until May 17th, 1836, when it disappeared 
from the sight of the most powerful telescopes of the time, 
and has not been seen since. But the astronomer can follow 
it with the eye of science with almost as much certainty as if 
he had it in the field of view of his telescope. We cannot yet 
fix the time of its return with certainty; but we know that it 
reached the farthest limit 
of its course, which ex- 
tends some distance be- 
yond the orbit of Nep- 
tune, about 1873, and 
that it is now on its re- 
turn journey. We pre- 
sent a diagram of its or- 
bit, showing its position 
in 1874. Its velocity 
will constantly increase 
from year to year, and 
we may expect it to Fl °- 9S -° rbIt of Halley * 

reach perihelion about the year 1911. The exact date cannot 
be fixed until the effect of the action of all the planets is com- 
puted, and this will be a greater labor than before, not only 
because greater accuracy will be aimed at, but because the 
action of more planets must be taken into account. When 
Clairaut computed the return of 1759, Saturn was the outer- 
most known planet. When the return of 1S35 was computed, 




386 TEE SOLAR SYSTEM. 

Uranus had been added to the list, and its action had to be 
taken into account. Since that time Neptune has been dis- 
covered; and the astronomer who computes the return of 1911 
must add its action to that of the other planets. By doing so, 
we may hope that the time of reaching perihelion will be pre- 
dicted within one or two days. 

The Lost Bields Comet. — Nothing could more strikingly il- 
lustrate the difference between comets and other heavenly 
bodies than the fact of the total dissolution of one of the for- 
mer. In 1826, a comet was discovered by an Austrian named 
Biela, which was found to be periodic, and to have been ob- 
served in 1772, and again in 1805. The time of revolution 
was found to be six years and eight months. In the next two 
returns, the earth was not in the right part of its orbit to ad- 
mit of observing the comet ; the latter was therefore not seen 
again till 1845. In November and December of that year 
it was observed as usual, without anything remarkable being 
noticed. But in January following, the astronomers of the 
Naval Observatory found it to have suffered an accident nev- 
er before known to happen to a heavenly body, and of which 
no explanation has ever been given. The comet had sepa- 
rated into two distinct parts, of quite unequal brightness, so 
that there were two apparently complete comets, instead of 
one. During the month following, the lesser of the two con- 
tinually increased, until it became equal to its companion. 
Then it grew smaller, and in March vanished entirely, though 
its companion was still plainly seen for a month longer. The 
distance apart of the two portions, according to the computa- 
tions of Professor Hubbard, was about 200,000 miles. 

The next return of the comet took place in 1852, and was, 
of course, looked for with great interest. It was found still 
divided, and the two parts were far more widely separated 
than in 1846, their distance having increased to about a mill- 
ion and a half of miles. Sometimes one part was the bright- 
er, and sometimes the other, so that it was impossible to de- 
cide which ought to be regarded as representing the principal 
comet. The pair passed out of view about the end of Sep- 






REMARKABLE COMETS. 38 i 

tember, 1852, and have not been seen since. They would, 
since then, have made three complete revolutions, returning in 
1859, 1865, and 1872. At the first of these returns, the rela- 
tive positions of the comet and the earth were so unfavorable 
that there was no hope of seeing the former. In 1865, it 
could not be found ; but it was thought that this might be due 
to the great distance of the comet from us. In 1872, the rela- 
tive positions were extremely favorable, yet not a trace of the 
object could be seen.* It had seemingly vanished, not into 
thin air, but into something of a tenuity compared with which 
the thinnest air was as a solid millstone. Some invisible frag- 
ments were, however, passing along the comet's orbit, and pro- 
duced a small meteoric shower, as will be explained in a later 
section. 

The Great Comet of 1843. — This remarkable comet burst 
suddenly into view in the neighborhood of the sun about the 
end of February, 1843. It was visible in full daylight, so that 
some observers actually measured the angular distance be- 
tween the comet and the sun. It was followed until the mid- 
dle of April. The most remarkable feature of the orbit of 
this comet has been already mentioned : it passed nearer the 
sun than any other known body — so near it, in fact, that, 
with a very slight change in the direction of its original mo- 
tion, it would actually have struck it. Its orbit did not cer- 
tainly deviate from a parabola. The most careful investigation 
of it — that of Professor Hubbard, of Washington — indicated 
a period of 530 years ; but the velocity which would produce 
'this period is so near the parabolic limit that the difference 
does not exceed the uncertainty of the observations. 

DonatC s Comet of 1858. — This great comet, one of the most 
magnificent of modern times, which hung in the western sky 
during the autumn of 1858, will be well remembered by all 
who were then old enough to notice it. It was first seen at 

* Just after the meteoric shower, Mr. Pogson, of Madras, obtained observa- 
tions of an object which, it was supposed, might have been a fragment of this 
comet. But the object was some two months behind the computed position of 
the comet, so that the identity of the two has never been accepted by astronomers. 



388 THE SOLAR SYSTEM. 

Florence, on June 2d, 1858, by Donati„who described it as a 
very faint nebulosity, about 3' in diameter. About the end 
of the month it was discovered independently by three Amer- 
ican observers : H. P. Tuttle, at Cambridge ; H. M. Parkhurst, 
at Perth Amboy, New Jersey ; and Miss Maria Mitchel, at 
Nantucket. During the first three months of its visibility it 
gave no indications of its future grandeur. No tail was no-, 
ticed until the middle of August, and at the end of that 
month it w r as only half a degree in length, while the comet 
itself was barely visible to the naked eye. It continued to 
approach the sun till the end of September, and during this 




Fig. 94.— Great comet of 1858. 

month developed with great rapidity, attaining its greatest 
brilliancy about the first half of October. Its tail was then 
40° in length, and 10° in breadth at its outer end, and of a 
curious feather-like form. About October 20th it passed so 
far south as to be no longer visible in northern latitudes ; but 
it was followed in the southern hemisphere until March fol- 
lowing. 

Observations of the position of this comet soon showed its 
orbit to be decidedly elliptic, with a period of about 2000 
years or less. A careful investigation of all the observations 
was made by Mr. G. W. Hill, who found a period of 1950 



EXCEEDS COMET, AXD THE RESISTING MEDIUM. 389 

years. If this period is correct, the comet must have appeared 
about ninety-two years before our era, and must appear again 
about the year 3808 ; but the uncertainty arising from the im- 
perfections of the observations may amount to fifty years. 

§ 4. Enckes Comet, and the Resisting Medium. 

The comet which in recent times has most excited the atten- 
tion of astronomers is that known as Encke's, from the astron- 
omer who first carefully investigated its motion. It was first 
seen in January, 1786, but the observations only continued 
through two days, and were insufficient to determine the orbit. 
In 1795, a comet was found by Miss Caroline Herschel, on 
which observations were continued about three weeks; but no 
very accurate orbit was derived from these observations. In 
1805, the same comet returned again to perihelion, but its iden- 
tity again failed to be recognized. As in the previous returns, 
the observations continued through less than a month. It was 
found, for the fourth time, by Pons, of Marseilles, in 1818. 
When its orbit was calculated, it was seen to coincide so 
closely with that of the comet of 1805 as to leave no doubt 
that the two were really the same body. But the first astron- 
omers who noticed this were unable to decide whether this 
was its first return since 1805, or whether it had in the mean 
time made several revolutions. 

The motions of the comet were now taken up by Encke, of 
Berlin, and investigated with a thoroughness before unknown. 
He found the period to be about 1200 days, four complete 
revolutions bavins: been made between 1805 and 1818. Know- 
ing this, there was no longer any difficulty in identifying the 
comet of 1795 as also being the same, three complete revolu- 
tions having been made between that date and 1S05. In the 
intermediate returns to perihelion, its position had been so 
unfavorable that it had not been observed at all. This result 
was received by astronomers with the greatest interest, because 
it was the first known case of a comet of short period. Its re- 
turn in 1822 was duly predicted, but it was found that when 
near its greatest brilliancy it would be visible only in the 



390 THE SOLAR SYSTEM. 

southern hemisphere. Happily, Sir Thomas Brisbane had an 
observatory at Paramatta, New South Wales, and his assistant, 
Rumker, was so fortunate as to find the comet. It was so 
near the position predicted by Encke that, by constantly point- 
ing the telescope in the direction predicted by that astronomer, 
the comet was in the field of view during its whole course. 

Encke continued to investigate the course of the comet dur- 
ing each revolution up to the time of his death, in 1865. At 
some returns it could not be seen, owing to its distance from 
the earth, or the otherwise unfavorable position of our planet ; 
but generally very accurate observations of its course were 
made. By a comparison of its motions with those which 
would result from the gravitation of the sun and planets, he 
found that the periodic time was constantly diminishing, and 
was thus led to adopt the famous hypothesis of Olbers, that 
the comet met with a resisting medium in space. The dimi- 
nution of the period was about two hours and a half in each 
revolution. The conclusion of Encke and Olbers was that the 
planetary spaces are filled with a very rare medium — so rare 
that it does not produce the slightest effect on the motion of 
such massive bodies as the planets. The comet being a body 
of extreme tenuity, probably far lighter than air, it might be 
affected by such a medium. The existence of this medium 
cannot, however, be considered as established by Encke's re- 
searches. In the first place, if we grant the fact that the 
time of revolution is continually diminishing, as maintained 
by the great German astronomer, it does not follow that a re- 
sisting medium is the only cause to which we can attribute it. 
But the main point is, that the computations on which Encke 
founded his hypothesis are of such intricacy as to be always 
liable to small errors, and their results cannot be received 
with entire confidence until some one else has examined the 
subject by new and improved methods. 

Such an examination is now being made by Dr. Yon Asten, 
of Pnlkowa ; and, although it is still unfinished, it seems like- 
ly, in the end, to confirm Encke's results, at least in part. Dr. 
Yon Asten commenced by calculating the motion of the comet 



EXCEEDS COMET, AND THE RESISTING MEDIUM. 301 

from the theory of gravitation during the period from 1 5 
to 1871, within which the comet made two entire revolutions, 
and was surprised to find that during this time there was no 
deviation from the computed positions which could be attrib- 
uted to the action of a resisting medium. But on tarrying 
the calculation back to 1861, he found that between that epoch 
and 1865 there must have been a retarding action like that 
supposed by Encke. Carrying his work forward to 1875, he 
found that between 1871 and 1875 there was once more evi- 
dence of a retardation about two-thirds as great as that found 
by Encke. The absence of such an action between 1865 and 
1871, therefore, seems quite exceptional, and difficult of ex- 
planation. 

To judge whether the deviations in the motion of Encke's 
comet are really due to a resisting medium, we should know 
whether the motions of other comets exhibit similar anom- 
alies. So far as is yet known, no other one does. There is 
at least one which ha> returned a sufficient number of times, 
and of which the motions have been computed with sufficient 
care, to lead to an entirely definite conclusion on this point. 
namely, the periodic comet of Faye, which has been investi- 
gated by Moller.* This comet was discovered in 1843 by the 
astronomer whose name it bears, and was soon found to move 
in an elliptic orbit, with a period of a little more than seven 
years. As it has been observed at several returns since, Moller 
investigated its motions with a view of finding whether its 
period was affected by any resisting medium. At first he 
thought there was such an effect, his general result being of 
the same nature with that reached by Encke. But on repeat- 
ing his calculations with the improved data afforded by a first 
calculation, he found that the result arose from the imperfec- 
tion of the latter, and that the comet really showed no sign of 
a change in its mean motion. It therefore seems certain that, 
if there is a resisting medium, it does not extend out far 
enough from the sun to meet the orbit of Faye's comet. But 

* Professor Axel Moller. director of the observatory at Lund, Sweden. 



392 THE SOLAR SYSTEM. 

this orbit lies wholly outside the orbit of Mars ; so that if the 
sun were surrounded bj an atmosphere extending out to Mars, 
and no farther, the cornet would never enter it. On the other 
hand, Encke's comet, when in perihelion, is nearer the sun 
than Mercury is, and might there meet a resisting medium 
which did not extend so far out as the orbit of Mars. We 
must therefore adopt one of two conclusions : either the cause 
which is supposed to affect the motion of Encke's comet is 
not a resisting medium, or, if it is such, it is confined to the 
neighborhood of the sun. Considering the improbability of 
the snn having any atmosphere which can extend to such a 
distance, the former should be deemed the more probable 
alternative. We can accept it the more readily, from the 
fact that comets in general exhibit deviations from their cal- 
culated orbits many times larger than those of the planets, so 
that an exact agreement between theory and observations can 
never be expected in the case of those bodies. 

The next subject to which we would ask the attention of 
the reader is that of the physical constitution of comets. But 
this subject can be discussed only in connection with another, 
to which, at first sight, it seems to have no relation, though 
so curious a relation has really been discovered as greatly to 
modify our views of what a comet probably is. We refer to 
the phenomena of meteors, meteoric showers, and shooting- 
stars, which next claim our attention. 

§ 5. Meteors and Shooting-stars. 

If we carefully watch the heavens on a cloudless night, we 
shall frequently see an appearance as of a star rapidly shoot- 
ing through a short space in the sky, and then suddenly dis- 
appearing. Three or four such shooting-stars may generally 
be seen in the course of an hour. Generally they are visible 
only for a second or two, but sometimes move slowly, and are 
seen much longer. Occasionally they are so brilliant as to 
illuminate the whole heavens, and they are then known as 
meteors — a term which is equally applicable to the ordinary 
shooting-stars. In general, they are seen only one at a time, 



METEORS AND SHOOTIXG-STAKS. 393 

and are so minute as hardly to attract attention. But they 
have on some occasions shown themselves in such numbers as 
to fill the beholders with terror, lest the end of the world had 
come. The Chinese, Arabian, and other historians have hand- 
ed down to us many accounts of such showers of meteors, 
which have been brought to light by the researches of Ed- 
ward Biot, Quetelet, Professor II. A. Newton, and others. As 
an example of these accounts, we give one from an Arabian 
writer : 

" In the year 599, on the last day of Moharrem, stars shot 
hither and thither, and flew against each other like a swarm 
of locusts ; this phenomenon lasted until daybreak ; people 
were thrown into consternation, and made supplication to the 
Most High : there was never the like seen except on the com- 
ing of the messenger of God, on whom be benediction and 
peace." 

In 1799, on the night of November 12th., a remarkable 
shower was seen by Humboldt and Bonpland, who were then 
on the Andes. Humboldt described the shower as commen- 
cing a little before two o'clock, and the meteors as rising above 
the horizon between east and north-east, and moving over tow- 
ards the south. From not continuing his observations long 
enough, or from some other cause, he failed to notice that the 
lines in which the meteors moved all seemed to converge tow- 
ards the same point of the heavens, and thus missed the dis- 
covery of the real cause of the phenomenon. 

The next great shower was seen in this country in 1833. 
All through the Southern States, the negroes, like the Arabs of 
a previous century, thought the end of the world had come at 
last. The phenomenon was observed very carefully at New 
Haven by Professor Olmsted, who worked out a theory of its 
cause. Although his ideas are in many respects erroneous, 
they were the means of suggesting the true theory to others. 
The recurrence of the shower at this time sns^ested to the 
astronomer Olbers the idea of a thirty-four-year period, and 
led him to predict a return of the shower in 1867. A few 
years before the expected time, the subject was taken up by 



394: THE SOLAR SYSTEM. 

Professor Newton, of Yale College, to whose researches our 
knowledge of the true cause of the phenomenon is very large- 
ly due. 

The phenomena of shooting-stars branch out in yet another 
direction. As we have described them, they are seen only in 
the higher and rarer regions of the atmosphere, far above the 
clouds: no sound is heard from them, nor does anything reach 
the surface of the earth from which the nature of the object 
can be inferred. But on rare occasions meteors of extreme 
brilliancy are followed by a loud sound, like the discharge of 
heavy artillery ; while on yet rarer occasions large masses of 
metallic or stony substances fall to the earth. These aerolites 
were the puzzle of philosophers. Sometimes there was much 
scepticism as to the reality of the phenomenon itself, it ap- 
pearing to the doubters more likely that those who described 
such things were mistaken than that heavy metallic masses 
should fall from the air. When their reality was placed be- 
yond doubt, many theories were propounded to account for 
them, the most noteworthy of which was that they were 
thrown from volcanoes in the moon. The problem of the 
motion of a body projected from the moon was investigated 
by several great mathematicians, the result being that such a 
body could not reach the earth unless projected with a veloci- 
ty far exceeding anything seen on our planet. 

When aerolites were examined by chemists and mineralo- 
gists, it was found that although they contained no new chem- 
ical elements, yet the combinations of these elements were 
quite unlike any found on the earth, so that they must have 
originated outside the earth. Moreover, these combinations 
exhibited certain characteristics peculiar to aerolites, so that 
the mineralogisf, from a simple examination and analysis of 
a substance, could detect it as part of such a body, though 
it had not been seen to fall. Great masses of matter thus 
known to be of meteoric origin have been found in various 
parts of the earth, especially in Northern Mexico, where, at 
some unknown period, an immense shower of these bodies 
seems to have fallen. 



METEORS AND SHOOTIXG-STARS. S9~j 

Cause of Shooting-stars. — It is now universally conceded that 
the celestial spaces are crowded with innumerable minute 
bodies moving around the sun in every possible kind of orbit. 
When we say crowded, we use the word in a relative sense ; 
they may not average more than one in a million of cubic 
miles, and yet their total number exceeds all calculation. Of 
the nature of the minuter bodies of this class nothing is cer- 
tainly known. But whatever they may be, the earth is con- 
stantly encountering them in its motion around the sun. They 
are burned by passing through the upper regions of our at- 
mosphere, and the shooting -star is simply the light of that 
burning. We shall follow Professor Newton in calling these 
invisible bodies meteor vids. 

The question which may be asked at this stage is, Why are 
these bodies burned ? Especially, how can they burn so sud- 
denly, and with so intense a light, as to be visible hundreds 
of miles away % These questions were the stumbling-block of 
investigators until they were answered, clearly and conclusive- 
ly, by the discovery of the mechanical theory of heat. It is 
now established that heat is only a certain form of motion ; 
that hot air differs from cold air only in a more rapid vibra- 
tion of its molecules, and that it communicates its heat to 
other bodies simply by striking them with its molecules, and 
thus setting their molecules in vibration. Consequently, if a 
body moves rapidly through the air, the impact of the air 
upon it ought to heat it just as warm air would, even though 
the air itself were cold. This result of theory has been ex- 
perimentally proved by Sir William Thomson, who found that 
a thermometer placed in front of a rapidly moving body rose 
one degree when the body moved through the air at the rate 
of 125 feet per second. With higher velocities, the increase 
of temperature was proportional to the square of the velocity, 
being 4 degrees with a velocity of 250 feet, 16 degrees with 
one of 500 feet per second, and so on. This result is in exact 
accordance with the mechanical theory of heat. To find the 
effective temperature to which a meteoroid is exposed in mov- 
ing through our atmosphere, we divide its velocity in feet per 



396 THE SOLAR SYSTEM. 

second by 125 ; the square of the quotient will give the tem- 
perature in degrees. 

Let us apply this principle to the case of the meteoroids. 
The earth moves in its orbit at the rate of 98,000 feet per 
second ; and if it met a meteoroid at rest, our atmosphere 
would strike it with this velocity. By the rule we have given 
for the rise of temperature (98,000 -^- 125) 2 = 784 2 = 600,000 
degrees, nearly. This is many times any temperature ever 
produced by artificial means. If, as will commonly be the 
case, the meteoroid is moving to meet the earth, the velocity, 
and therefore the potential temperature, will be higher. We 
know that the meteoroids which produce the November show- 
ers already described move in a direction nearly opposite that 
of the earth with a velocity of 26 miles per second, so that the 
relative velocity with whidh the meteoroids meet our atmos- 
phere is 44 miles per second. By the rule we have given, 
this velocity corresponds to a temperature of between three 
and four million degrees. We do not mean that the meteor- 
oids are actually heated up to this temperature, but that the 
air acts upon them as if it were heated up to the point men- 
tioned ; that is, it burns or volatilizes them in less than a sec- 
ond with an enormous evolution of light and heat, just as a 
furnace would if heated to a temperature of three million de- 
grees. It is not at all necessary that the body should be com- 
bustible ; the light and heat of ordinary burning are nothing 
at all compared with the deflagration which such a tempera- 
ture would cause by acting on the hardest known body. A 
few grains of platinum or iron striking the atmosphere with 
the velocity of the celestial motions might evolve as much light 
and heat as are emitted by the burning of a pint of coal-oil or 
several pounds of gunpowder; and as the whole operation is 
over in a second, we ma} 7 imagine how intense the light must be. 

The varied phenomena of aerolites, meteors, shooting-stars, 
and meteoric showers depend solely on the number and nat- 
ure of the meteoroids which give rise to them. If one of 
these bodies is so large and firm as to pass through the atmos- 
phere and reach the earth without being destroyed by the po- 



METEORS AXD SHOOTIXG-STARS. 397 

tential heat, we have an aerolite. As this passage only occu- 
pies a few seconds, the heat has not time to penetrate far into 
the interior of the body, but expends itself in melting and vol- 
atilizing the outer portions. When the body first strikes the 
denser portion of the atmosphere, the resistance becomes so 
enormous that the aerolite is frequently broken to pieces with 
such violence that it seems to explode. Further color is given 
to the idea of an explosion by the loud detonation which fol- 
lows, so that the explosion is frequently spoken of as a fact, 
and as the cause of the detonation. Really, there is good rea- 
son to believe that both of these phenomena are due to the 
body striking the air with a velocity of ten, twenty, or thirty 
miles a second. 

If, on the other hand, the meteoroid is so small or so fusible 
as to be dissipated in the upper regions of the atmosphere, we 
have a common shooting-star, or a meteor of greater or less 
brilliancy. Very careful observations have been made from 
time to time, with a view of finding the height of these bodies 
above the earth at their appearance and disappearance. An 
attempt of this kind was made by the Naval Observatory on 
the occasion of the meteoric shower of November 13th. 1867, 
when Professor Ilarkness was sent to Richmond to map the 
paths of the brighter meteors as seen from that point. By 
comparing these paths with those mapped at Washington, the 
parallaxes, and thence the altitudes, of these bodies were de- 
termined. The lightning-like rapidity with which the mete- 
ors darted through their course rendered it impossible to ob- 
serve them with astronomical precision ; but the general re- 
sult was that they were first seen at an average height of 75 
miles, and disappeared at a height of 55 miles. There was 
no positive evidence that any meteor commenced at a height 
much greater than 100 miles. It is remarkable that this cor- 
responds very nearly to the greatest height at which the most 
brilliant meteors are ever certainly seen. These phenomena 
seem to indicate that our atmosphere, instead of terminating 
at a height of ±5 miles, as was formerly supposed, really ex- 
tends to a heio'ht of between 100 and 110 miles. 



398 THE SOLAR SYSTEM. 

The ordinary meteors, which we may see on every clear 
evening, move in every direction, thus showing that their or- 
bits lie in all possible positions, and are seemingly scattered 
entirely at random. But the case is quite different with those 
meteoroids which give rise to meteoric showers. Here we 
have a swarm of these bodies, all moving in the same direc- 
tion in parallel lines. If we mark, on a celestial globe, the 




Fig. 95.— Meteor paths, illustrating the radiant point. 

apparent paths of the meteors which fall during a shower, or 
if we suppose them marked on the celestial sphere, and then 
continue them backwards, we shall find them all to meet in 
the same point of the heavens. This is called the radiant 
point. It always appears in the same position, wherever the 
observer is situated, and does not partake of the diurnal mo- 



RELATIONS OF COMETS AND METEOROIDS. 399 

tion of the earth ; that is, as the stars seem to move towards 
the west in their diurnal course, the radiant point moves with 
them. The point in question is purely an effect of perspec- 
tive, being the "vanishing point" of the parallel lines in 
which the meteors really move. These lines do not appear 
in their real direction in space, but are seen as projected on 
the celestial sphere. A good visible illustration of the effect 
in question may be afforded by looking upwards and watch- 
ing falling snow during a calm. The flakes which are fall- 
ing directly towards the observer do not seem to move at all, 
while the surrounding flakes seem to separate from them on 
all sides. So with the meteoric showers. A meteor coming 
directly towards the observer does not seem to move at all. 
and marks the radiant point from which all the others seem 
to diverge. The great importance of the determination of 
the radiant point arises from the fact that it marks the direc- 
tion in which the meteors are moving relatively to the earth, 
and thus affords some data for determining their orbits. 

§ 6. Relations of Comets and Meteoroids. 

We have now to mention a series of investigations which 
led to the discovery of a curious connection between meteor- 
oids and comets. These investigations were commenced by 
Professor Newton on the November meteoric showers. Tra- 
cing back the historical accounts of these showers to which 
we have already alluded, he found that the thirty-three-year 
period, which had been suspected by Olbers, was confirmed by 
records reaching back a thousand years. Moreover, the show- 
ers in question occurred only at a certain time of the year : in 
1799 and 1833, it was on November 12th or November 13th. 
In other words, the shower occurred only as the earth passed 
a certain point of its orbit. But this point was found not to 
be always the same, the showers being found to occur about 
a couple of days earlier every century as they were traced 
back. The principal conclusions to which these facts led 
were as follows : 

1. That the swarm of meteoroids which cause the Novem- 

27 



400 THE SOLAR SYSTEM. 

ber showers revolve around the sun in a definite orbit, which 
intersects the orbit of the earth at the point which the latter 
now passes on November 13th. 

2. The point of intersection of the two orbits moves for- 
wards about 52" per annum, or nearly a degree and a half a 
century, owing to a change in the position of the meteoric 
orbit. 

3. The swarm of meteoroids is not equally scattered all 
around their orbit, but the thickest portion extends along 
about one-fifteenth of the orbit. 

4. The earth meets this swarm, on the average, once in 
33.25 years. At other times the swarm has not arrived at 
the point of crossing, or has already passed it, and a meteoric 
shower cannot occur unless the earth and the swarm cross at 
the same time. 

Professor' Newton did not definitely determine the time of 
revolution of the meteors in their orbit, but showed that it 
must have one of five values. The greatest of these values, 
and the one which it seems most natural to select, is that of 
the mean interval between the showers, or 33^ years. Adopt- 
ing this period, it would follow that between 1799, when 
Humboldt saw the meteoric shower, and 1833, when it was 
seen throughout the United States, the swarm of meteoroids 
had been flying out as far as the planet Uranus in a very el- 
liptical orbit, and returning again. But the periodic time 
might also be one year and about eleven days. Then the 
group which Humboldt saw on November 12th, 1799, would 
not reach the same point of its orbit until November 23d, 
1800, when the earth would have passed by. Passing 11 days 
later every year, it would make about 33 revolutions in 34 
years, ^and thus would pass about the middle of November 
once more, and another shower would occur. In a word, giv- 
ing exact numbers, we might suppose that in the period of 
33J years the meteoroids made one revolution, or 32 J, 34J, 
65^, or 67-J revolutions, and the conditions of the problem 
would be equally satisfied. 

At the same time, Professor Newton gave a test by which 



RELATIONS OF COMETS AND METEOROIDS. 401 

the true time could be determined. As we have said, he 
showed that the node of the orbit changed its position 52'' a 
century, and there could be no doubt that this change was 
due to the attraction of the planets. If, then, the effect of 
this attraction was calculated for each of the rive orbits, it 
would be seen which of them would give the required change. 
This was done by Professor Adams, of England, and the result 
was that the thirty-three-year period, and that alone, was ad- 
missible. 

These researches of Professor Newton were published in 
1864, and ended with a prediction of the return of the shower 
on November 13th of one or more of the three following 
years — probably 1866. This prediction was verified by a re- 
markable meteoric shower seen in Europe on that very day, 
which, however, was nearly over before it could become visi- 
ble in this country. On the same date of the year following, 
a shower was visible in this country, and excited great public 
interest. From the data derived from the first of these show- 
ers, Schiaparelli, an Italian astronomer, was led to the discovery 
of a remarkable relation between meteoric and cometary orbits. 
Assuming the period of the November meteoroids to be 33J 
years, he computed the elements of their orbit from the ob- 
served position of the radiant point. A similar computation 
was made by Leverrier, and the results were presented to the 
French Academy of Sciences on January 21st, 1S67. 

The exact orbit which these bodies followed through space, 
crossing the eartlrs orbit at one point, and extending out 
beyond the planet Uranus at another, was thus ascertained. 
But, as these bodies were absolutely invisible, no great inter- 
est seemed to attach to their orbit until it was found that a 
comet was moving in that very orbit. This was a faint tele- 
scopic comet discovered by Tempel, at Marseilles, in Decem- 
ber, 1865. It was afterwards independently discovered by 
Mr. H. P. Tuttle, at the Naval Observatory, Washington. It 
passed its perihelion in January, and, receding from the sun, 
vanished from sight in March. It was soon found to move 
in an elliptic orbit, but, owing to the uncertainty of observa- 



402 



THE SOLAR SYSTEM. 



1*111 



V/*A/V(/.$ 



tions on such a body, 
there was at first some 
disagreement as to the 
exact periodic time. 
The subject was taken 
up by Dr. Oppolzer, of 
Vienna, who, in Janu- 
ary, 1867, was able to 
present a definitive or- 
bit of the comet, which 
was published in the As- 
tronomische Nachrichten 
on the 28th of that 
month. We now pre- 
sent the orbit of the 
comet, as found by Op- 
polzer, and that of the 
meteors, as found by 
Leverrier, premising 
tli at these orbits were 
computed and publish- 
ed within a few days 

Pig. 96— Orbit of November meteors and the comet °* each Other, without 

ofl861 - any knowledge on the 

part of either astronomer of the results obtained by the other : 






The Comet. 


Meteoroids. 


Period of revolution 


33.18 vrs. 

0.9054 

0.9765 

162° 42' 

51° 26' 

42° 24' 


33.25 yrs. 
0.9044 
0.9890 
165° 19' 

51° 18' 
Near node. 


Eccentricity 

Perihelion distance 


Inclination of orbit 


Longitude of the node 

Longitude of perihelion 





The similarity of these orbits is too striking to be the result 
of chance. The only element of which the values differ ma- 
terially is the inclination, and this difference proceeds from 
Leverrier not having used a very exact position of the radiant 
point in making his computations. Professor Adams found 
by a similar calculation that the inclination of the orbit of the 






RELATIONS OF COMETS AND METEOROIDS. 



403 



meteoroids was 163° 14', only half a degree different from that 
of the orbit of Temper's eomet. The result of these investiga- 
tions was as follows : 

The November meteoric showers arise from the earth encountering 
a swarm of particles following 
Tempel 1 s comet in its orbit. 

"When this faet came out, 
Schiaparelli had been working 
on the same subject, and had 
come to a similar conclusion 
with regard to another group 
of meteors. It had long been 
known that about August 9th 
of every year an unusual num- 
ber of meteors shoot forth from 
the constellation Perseus. At 
times these showers have been 
inferior only to those of No- 
vember. Thus, on August 0th, 
1798, they succeeded each oth- 
er so rapidly as to keep the 
eye of the observer almost con- 
stantly engaged, and several 
hundred may nearly always be 
counted on the nights of the 
9th, 10th, and 11th. These 
August meteors are remarka- 
ble in that they leave trails of 
luminous vapor which often 
last several seconds. Assum- 
ing the orbit of this group to 
be a parabola, it was calculated 
by Schiaparelli, and is substan- 
tially the same with that of a 
comet observed in 1S62. The 
following are the elements of 

the Orbits of the two bodie^ * Fig. 9T.-Orbit of the third comet of 1S62. 




404 



THE SOLAR SYSTEM. 





Comet II., 
1862. 


August 
Meteoroids. 


Perihelion distance 

Inclination of orbit 

Longitude of the node 

Longitude of the perihelion 


0.9626 
113° 35' 
137° 27' 
344° 41' 


0.9643 
115° 57' 
138° 16' 
343° 28' 



It appears that the August meteors are caused by a long 
stream of bodies following the second comet of 1862 in its 
orbit, or, rather, moving in the same orbit with it. The orbit 
of this comet is decidedly elliptic; the difference from the 
parabola is, however, too small to be determined with great 
precision. According to Oppolzer, the period derived from 
the observations would be 124 years, which, however, may be 
ten years or more in error. 

A third striking case of the connection between comets and 
meteors w T hich we are showing is afforded by the actual pre- 
diction of a meteoric shower on the night of November 27th, 
1872. I have already described Biela's comet as first break- 
ing into two pieces and then entirely disappearing, as thougli 
its parts had become completely scattered. This is one of 
the few comets which may come very near the earth, the lat- 
ter passing the orbit of the comet on November 27th of each 
year. By calculation, the comet should have passed the point 
of crossing early in September, 1872, while the earth reached 
the same point between two and three months later. Judg- 
ing from analogy, there was every reason to believe that the 
earth would encounter a stream of meteoroids consisting of the 
remains of the lost comet, and that a small meteoric shower 
would be the result. Moreover, it was shown that the mete- 
ors would all diverge from a certain point in the constellation 
Andromeda, as the radiant point, because that would be the di- 
rection from which a body moving in the orbit of the comet 
would seem to come. The prediction was fully verified in 
every respect. The meteors did not compare, either in num- 
bers or brilliancy, with the great displays of November ; but, . 
though faint, they succeeded each other so rapidly that the 
most casual observer could not fail to notice them, and they 
all moved in the predicted direction. 



RELATIONS OF COMETS AND METEOROIDS. 4"5 

That the meteoroids in these cases originally belonged to 
the comet, few will dispute. Accepting this, the phenomena of 
the November showers lead to the conclusion that the comet 
of 1SG6, with which they are associated, was not an original 
member of our system, but has been added to it within a 
time which, astronomically speaking, is still recent. The sep- 
arate meteoroids which form the stream will necessarily have 
slightly different periodic times. Such being the case, they 
will, in the course of many revolutions, gradually scatter them- 
selves around their entire orbit; and then we shall have an 
equal meteoric shower on every 13th of November. This 
complete scattering seems to have actually taken place in the 
case of the August meteoroids, since we have nearly the same 
sort of shower on every Oth or 10th of August. But in the 
case of the November meteors, the stream is not yet scattered 
over one-tenth of the orbit. If we suppose that the motion- 
of the slowest and the swiftest bodies of the stream only dif- 
fer by a thousandth part of their whole amount — which is not 
an unreasonable supposition — it would follow that the stream 
had only made about 100 revolutions around the sun, and had 
therefore been revolving only about 3300 years. Though this 
number is purely hypothetical, we may say with confidence 
that the stream has not been in existence many thousand 
years. 

This opinion is strongly supported by the fact that the orbit 
of this meteoric comet passes very near that of Uranus as well 
as that of the earth, so that there is reason to believe that it 
was introduced into our system by the attraction of one of 
these planets, probably of Uranus. If the comet is seen on its 
next return, in 1S99, we may hope that its periodic time will 
be determined with sufficient accuracy to enable us to fix with 
some probability the exact date at which Uranus brought it 
into our system. Indeed, Leverrier has attempted to do this 
already, having fixed upon the year 126 of our era as the 
probable date of this event ; but, unfortunately, neither the 
position of the orbit nor the time of revolution is yet known 
with such accuracy as to inspire confidence in this result. 



406 THE SOLAR SYSTEM. 

The idea that. this November group is something compara- 
tively new is strengthened by a comparison with that which 
produces the August meteors, where we find a decided mark 
of antiquity. Here the swiftest of the group has, in the course 
of numerous revolutions, overtaken the slowest, so that the 
group is now spread almost equally around the entire orbit. 
The time of revolution being, in this case, more than a cen- 
tury, this equal distribution would take a much longer time 
than in the other case, where the period is only thirty-three 
years ; so that we can say, with considerable probability, that 
the August group has been in our system at least twenty 
times as long as the November group. 

§ 7. The Physical Constitution of Comets. 

A theory of the physical constitution of comets, to be both 
complete and satisfactory, must be founded on the properties 
of matter as made known to us here at the surface of the 
earth. That is, we must show what forms and what combina- 
tions of known substances would, if projected into the celes- 
tial spaces, present the appearance of a comet. Now, this has 
never yet been completely done. Theories without number 
have been propounded, but they fail to explain some of the 
phenomena, or explain them in a manner not consistent with 
the known laws of matter or force. We cannot stop even to 
mention most of these theories, and shall therefore confine our 
attention to those propositions which are to some extent sus- 
tained by facts, and which, on the whole, seem to have most 
probability in their favor. 

The simplest form of these bodies is seen in the telescopic 
comets, which consist of minute particles of a cloudy or vapor- 
ous appearance. Now, we know that masses which present 
this appearance at the surface of the earth, where we can ex- 
amine them, are composed of detached particles of solid or 
liquid matter. Clouds and vapor, for instance, are composed 
of minute drops of water, and smoke of very minute particles 
of carbon. Analogy would lead us to suppose that the tele- 
scopic comets are of the same constitution. They are gener- 






THE PHYSICAL CONSTITUTION OF COMETS. 

ally tens of thousands of miles in diameter, and yet of such 
tenuity that the smallest stars are seen through them. The 
strongest evidence of this constitution is, however, afforded bj 
the phenomena of meteoric showers described in the last 
tion. We have seen that these are caused by our atmosphere 
encountering the debris of comets, and this debris presents it- 
self in the form of -detached meteoroids, of very small magni- 
tude, but hundreds of miles apart. 

The only alternative to this theory is that the comet is a 
mass of true gas, continuous throughout its whole extent. 
This gaseous theory derives its main support from the spec- 
troscope, which shows the spectrum of the telescopic con 
to consist of bright bands, the mark of an incandescent gas. 
Moreover, the resemblance of these bands to those produced 
by the vapor of carbon is so striking that it is quite common 
among spectroscopists to speak of a comet as consisting of 
the gas of some of the compounds of carbon. But there are 
several difficulties which look insuperable in the way of the 
theory that a comet is nothing but a mass of gas. In the 
first place, the elastic force of such a mass would cause it 
to expand beyond all limits when placed in a position where 
there is absolutely no pressure to confine it, as in the celestial 
spaces. Again, a gas cannot, so far as experiment has ever 
gone, shine by its own light until it is heated to a high tem- 
perature, far above any that can possibly exist at distances 
from the sun so great as those at which comets have been 
situated when under examination with the spectroscope. Fi- 
nally, in the event of a purely gaseous comet being broken 
up and dissipated, as in the case of Biela's comet, it is hardly 
possible to suppose that it would separate into innumerable 
widely detached pieces, as this comet did. The gaseous the- 
ory can, therefore, not be regarded as satisfactory. It may be 
that comets will hereafter be found to consist of some combi- 
nation of solid and gaseous matter, the exact nature of which 
is not yet determined ; or it may be that this matter is of a 
nature or in a form wholly unlike anything that we are ac- 
quainted with or can produce here on the earth. As the case 



408 THE SOLAR SYSTEM. 

now stands, we must regard the spectrum of a comet as some- 
thing not yet satisfactorily accounted for. 

When we turn from telescopic comets to those brilliant 
ones which exhibit a nucleus and a tail, we can trace certain 
operations which are not seen in the case of the others. What 
the nucleus is — whether it is a solid body several hundred miles 
in diameter, or a dense mass of the same materials which com- 
pose a telescopic comet — we are quite unable to say. But 
there can hardly be any reasonable doubt that it is composed 
of some substance which is vaporized by the heat of the solar 
rays. The head of such a comet, when carefully examined 
with the telescope, is found to be composed of successive en- 
velopes or layers of vapor ; and when these envelopes are 
watched from night to night, they are found to be gradually 
rising upwards, growing fainter and more indistinct in out- 
line as they attain a greater elevation, until they are lost in 
the outlying parts of the coma. These rising masses form the 
fan-shaped appendage described in a preceding section. 

The strongest proof that some evaporating process is going 
on from the nucleus of the comet is afforded by the move- 
ments of the tail. It has long been evident tliaf the tail could 
not be an appendage which the comet carried along with it, 
and this for two. reasons: first, it is impossible that there could 
be any cohesion in a mass of matter of such tenuity that the 
smallest stars could be seen through a million of miles of it, 
and which, besides, constantly changes its form ; secondly, as 
a comet flies around the sun in its immediate neighborhood, 
the tail appears to move from one side of the sun to another 
with a rapidity which would tear it to pieces, and send the 
separate parts flying off in hyperbolic orbits, if the movement 
were real. The inevitable conclusion is that the tail is not a 
fixed appendage of the comet, which the latter carries with it, 
but a stream of vapor rising from it, like smoke from a chim- 
ney. As the line of smoke which we now see coming from 
the chimney is not the same which we saw a minute ago, be- 
cause the latter has been blown away and dissipated, so we do 
not see the same tail of a comet all the time, because the mat- 



THE PHYSICAL CONSTITUTION OF COMETS 409 

tor which makes up the tail is constantly streaming outwards, 
and constantly being replaced by new vapor rising from the 
nucleus. The evaporation is, no doubt, due to the heat of the 
sun, for there can be no evaporation without heat, and the 
tails of comets increase enormously as they approach the sun. 
Altogether, a good idea of the operations going on in a comet 
will be obtained if we conceive the nucleus to be composed of 
water or other volatile fluid which is boiling away under the 
heat of the sun, while the tail is a column of steam rising 
from it. 

We now meet a question to which science has not yet been 
able to return a conclusive answer. Why does this mass of 
vapor always fly away from the sun ? That the matter of the 
comet should bo vaporized by the sun's rays, and that the nu- 
cleus should thus be enveloped in a cloud of vapor, is perfect- 
ly natural, and entirely in accord with the properties of mat- 
ter which we observe around us. But, according to all known 
laws of matter, this vapor should remain around the head, ex- 
cept that the outer portions would be gradually detached and 
thrown off into separate orbits. There is no known tendency 
of vapor, as seen on the earth, to recede from the sun. and no 
known reason why it should so recede in the celestial spa 
Various theories have been propounded to account for it ; but 
as they do not rest on causes which we have verified in other 
cases, they must be regarded as purely hypothetical. 

The first of these explanations, in the order of time, is due 
to Kepler, who conceived the matter of the tail to be driven 
off by the impulsion of the solar rays, which thus bleached 
the comet as they bleach cloths here. If light were an emis- 
sion of material particles, as Xewton supposed it to be, this 
view would have some plausibility. But light is now con- 
ceived to consist of vibrations in an ethereal medium ; and 
there is no known way in which they could exert any propel- 
ling force on matter. Two or three years ago. it was for 
a while supposed that the " radiometer " of Mr. Grookes might 
really indicate such an action of the solar rays upon matter 
in a vacuum, but it is now found that the action exhibited is 



410 THE SOLAB SYSTEM. 

really due to a minute quantity of air left in the instrument. 
Had Mr. Crookes shown that the motion of his radiometer 
was really due to die impulsion of the solar rays, we might 
be led to the remarkable conclusion that Kepler's theory, 
though rejected for more than two centuries, was, after all, 
quite near the truth. 

Sir Isaac Newton, being the author of the emission theory 
of light, could not dispute the possibility of Kepler's views 
being correct, but nevertheless gave the preference to anoth- 
er hypothesis. He conceived the celestial spaces to be filled 
with a very rare medium, through which the sun's rays passed 
without heating it, as they pass through cold air. But the 
comet being warmed up by the rays, the medium surrounding 
it is warmed up by contact, and thus a warm current is sent 
out from the comet, just as a current of warm air rises from 
a heated body on the surface of the earth. This current car- 
ries the vapor of the comet with it, and thus gives rise to the 
tail in the same way that the current of warm air rising from 
a chimney carries up a column of smoke. It has long been 
established that there is no medium in the planetary spaces 
in which such an effect as this is possible : Newton's theory 
is, therefore, no longer considered. 

In recent times, Zollner has endeavored to account for the 
tail of the comet by an electrical action between the sun and 
the vapor rising from the nucleus of the comet. The various 
papers in which he has elaborated his views of the constitu- 
tion of comets are marked by profound research ; and we 
must regard his theories as those which, on the whole, most 
completely explain all the phenomena. But they still lack 
the one thing needful to secure their reception : there is no 
evidence that the sun acts as an electrified body ; and until 
such evidence is adduced by experiment, or by observation on 
other bodies than comets, the electric theory of the comet's 
tail can only be regarded as a more or less probable hypothe- 
sis. Indeed, some physicists claim that any such electric ac- 
tion in the planetary spaces is impossible. Before any theory 
can be definitely settled upon, accurate observations must be 



THE PHYSICAL CONSTITUTION OF COMETS. 411 

made upon the tails of comets with a view of learning the 
law according to which the vapor is repelled from the sun. 
Such observations were made by Bessel on Ilalley's comet in 
1835, and by various observers on the great cornet of 1858. 
The former were investigated by Bessel himself, and the lat- 
ter by several mathematicians, among them Professor Peirce, 
whose results are found in a paper communicated to the 
American Academy in 1859. He found the repulsive force 
of the sun upon the particles which form the front edge of 
the tail to be 1-J- times its attractive force upon ordinary 
bodies at the same distance. It seemed constantly to diminish 
as the back edge of the tail was approached ; but, owing to 
the poor definition of this edge, and the uncertainty whether it 
was composed of a continuous stream of particles, the amount 
of the diminution could not be accurately fixed. The suc- 
cessive envelopes were found to ascend uniformly towards 
the sun at the rate of about thirty-five miles an hour. Bond, 
from a careful examination of all the observations, was led to 
the result that the rate of ascent diminished as the height 
became greater. 

An apparently necessary conclusion from this constant evap- 
oration and expulsion of vapor from comets with tails is, that 
such bodies are constantly wasting away when in the neigh- 
borhood of the sun. This conclusion is strengthened by the 
fact that not a single comet Of very short period has a consid- 
erable tail, the probability being that all the volatile matter 
which once went to form the tail has been evaporated. In- 
deed, from the descriptions of the old chroniclers, it has been 
supposed that Ilalley's comet had a much more conspicuous 
tail at the time of its earliest recorded apparitions than it lias 
exhibited at its last few returns. There is, however, no neces- 
sity for supposing the diminution so rapid as this, for the 
amount of matter really necessary to make the most splendid 
tail is so extremely small that a comet might lose it a hundred 
times over without becoming perceptibly smaller. This con- 
stant loss of matter through the tail affords an additional 
ground for the view that comets in general are visitors intro- 



412 THE SOLAR SYSTEM. 

duced into our system by the action of the planets. If, for 
instance, such a comet as Halley's had been a member of our 
system for millions of years, and had returned to perihelion a 
hundred thousand times, all its volatile matter must long ago 
have evaporated. 

The question of the mass and density of comets is also one 
of those on which it is difficult to reach satisfactory conclu- 
sions. We cannot certainly decide from mere telescopic ob- 
servation whether the nucleus is a single large body, like a 
planet or satellite, or whether it is merely the densest part of 
an immense cloud of meteoroids. The mass of nebulous mat- 
ter which surrounds the nucleus increases so gradually as we 
approach the central parts, that it is hardly possible to decide 
where the nucleus begins : the more powerful the telescope, 
the smaller the nucleus generally appears. Moreover, in the 
same comet, the apparent magnitude of the nucleus is subject 
to immense variations, thus showing that it cannot be a solid 
body out to its apparent limits. If we considered only this 
circumstance, and the general analogy with telescopic comets, 
we should say that even the densest part of the comet was 
nothing but a cloud of solid or liquid particles so thick that it 
looked solid, as a cloud does in our sky. But if this was the 
case, as Professor Peirce showed in his investigations of the 
comet of 1858, the comets of 1680 and of 1843 must have 
been completely pulled apart by the enormous tidal forces 
generated by their near approach to the sun. In the opinion 
of this investigator, the fact that they went through such an 
ordeal shows them to be of metallic density. 

The question is frequently asked, What would be the effect 
if a comet should strike the earth ? This would depend upon 
what sort of a comet it was, and what part of the comet came 
in contact with our planet. The latter might pass through 
the tail of the largest comet without the slightest effect being 
produced, the tail being so thin and airy that a million miles 
thickness of it looks only like gauze in the sunlight. It is 
not at all unlikely that such a thing may have happened with- 
out ever being noticed. A passage through a telescopic comet 



THE ZODIACAL LI CUT. 



would be accompanied by a brilliant meteoric shower, prob- 
ably a far mure brilliant one than has ever been recorded. 
No more serious danger would be encountered than that aris- 
ing from a possible fall of meteorites. But a collision between 
the nucleus of a large comet and the earth might be a serious 
matter. If, as Professor Peirce supposes, the nucleus is a solid 
body of metallic density, many miles in diameter, the effect 
where the comet struck would be terrific beyond conception. 
At the first contact in the upper regions of the atmosphere 
the whole heavens would be illuminated with a resplendence 
beyond that of a thousand suns, the sky radiating a light which 
would blind every eye that beheld it, and a heat which would 
melt the hardest rocks. A few seconds of this, while the hi 
body was passing through the atmosphere, and the collision at 
the earth's surface would in an instant reduce everything there 
existing to fiery vapor, and bury it miles deep in the solid 
earth. Happily, the chances of such a calamity are so minute 
that they need not cause the slightest uneasiness. There i- 
hardly a possible form of death which is not a thousand time- 
more probable than this. So small is the earth in comparison 
with the celestial spaces, that if one should shut his eyes and 
fire a gun at random in the air, the chance of bringing down 
a bird would be better than that of a comet of any kind strik- 
ing the earth. 

§ 8. 77m? Zodiacal Light 

This object consists of a very soft, faint column of light, 
which may be seen rising from the western horizon after twi- 
light on any clear winter or spring evening: it may also be 
seen rising from the eastern horizon just before daybreak in 
the t summer or autumn. It really extends out on each side 
of the sun, and lies nearly in the plane of the ecliptic. The 
reason it cannot be well seen in the summer and autumn 
evenings is, that in our latitudes the course of the ecliptic in 
the south-west is, during those seasons, so near the horizon that 
the light in question is extinguished by the great thickness of 
atmosphere through which it has to pass. Near the equator, 



414 THE SOLAR SYSTEM. 

where the ecliptic always rises high above the horizon, the 
light can be seen about equally well all the year round. It 
grows fainter the farther it is from the sun, and can gener- 
ally be traced to about 90° from that luminary, when it grad- 
ually fades away. But in a very clear atmosphere, between 
the tropics, it has been traced all the way across the heavens, 
from east to west, thus forming a complete ring. 

Such is the zodiacal light as it appears to the eye. Put- 
ting its appearances all together, we may see that it is due to 
a lens -shaped appendage of some sort surrounding the sun, 
and extending out a little beyond the earth's orbit. It lies 
very nearly in the plane of the ecliptic, but its exact position 
is difficult to determine, not only owing to its indistinct out- 
line, but because in northern latitudes the southern edge will 
be dimmed by the greater thickness of atmosphere through 
which it is seen, and thus the light will look farther north 
than it really is. The nature of the substance from which 
this light emanates is entirely unknown. Its spectrum has 
been examined by several observers, some of whom have re- 
ported it as consisting of a single yellow line, and therefore 
arising from an incandescent gas. This would indicate a len- 
ticular-shaped atmosphere of inconceivable rarity surrounding 
the sun, and extending out near the plane of the ecliptic be- 
yond the orbit of the earth. But Professor Wright, of Yale 
College, who has made the most careful observations of this 
spectrum, finds it to be continuous. For several reasons, too 
minute to enter into now, this observation seems to the writer 
more likely to be correct. Accepting it, we should be led to 
the conclusion that the phenomenon in question is due to re- 
flected sunlight, probably from an immense cloud of meteor- 
oids filling up the space between the earth and sun. But fur- 
ther researches must be made before a conclusive result can 
be reached. 



PART IV.— THE STELLAR UNIVERSE. 



INTRODUCTORY REMA RKS. 

Hitherto our attention lias been principally occupied with 
the bodies which surround our sun and make up the solar - 
tern. Notwithstanding the immense distances at which tl 
bodies are found, we may regard them, in comparison with the 
fixed stars, as an isolated family immediately surrounding us, 
since a sphere as large as the whole solar system would only 
appear as a point to the vision if viewed from the nearest 
star. The space which separates the orbit of Neptune from 
the fixed stars and the fixed stars from each other is, so far as 
we can learn, entirely void of all visible matter, except occa- 
sional waste nebulous fragments of a meteoric or cometarv 
nature which are now and then drawn in by the attraction of 
our sun. 

The widest question which the study of the stars presents 
to us may be approached in this way : We have seen, in our 
system of sun, planets, and satellites, a very orderly and 
beautiful structure, every body being kept in its own orbit 
through endless revolutions bv a constant balancing of oravi- 
tatins: and centrifugal forces. Do the millions of suns and 
clusters scattered through space, and brought into view by the 
telescope, constitute a greater system of equally orderly struct- 
ure ? and, if so, what is that structure \ If we measure the 
importance of a question, not by its relations to our interests 
and our welfare, but by the intrinsic greatness of the subject 
to which it relates, then we must regard this question as one 
of the noblest with which the human mind has ever been 

2S 



416 THE STELLAB UNIVERSE. 

occupied. In piercing the mystery of the solar system, and 
showing that the earth on which we dwell was only one of 
the smaller of eight planets which move around the sun, we 
made a great step in the way of enlarging our ideas of the 
immensity of creation and of the comparative insignificance 
of our sublunary interests. But when, on extending our view, 
we find our sun to be but one out of unnumbered millions, we 
see that our whole system is but an insignificant part of crea- 
tion, and that we have an immensely greater fabric to study. 
When we have bound all the stars, nebulae, and clusters which 
our telescopes reveal into a single system, and shown in what 
manner each stands related to all the others, we shall have 
solved the problem of the material universe, considered, not in 
its details, but in its widest scope. 

From the time that Copernicus showed the stars to be self- 
luminous bodies, situated far outside of our solar system, the 
question thus presented has occupied the attention of the phil- 
osophical class of astronomers. The original view, which has 
been the starting-point of all speculation on the subject, we 
have described in the Introduction as that of a spherical uni- 
verse. The apparent sphericity of the vault of heaven, the 
uniformity of the diurnal revolution, and the invariability of 
the relative positions of the stars, all combined to strengthen 
the idea that the latter were set on the interior surface of a 
hollow sphere, having the earth or the sun in its centre. This 
sphere constituted the firmament of the ancients, outside of 
which was situated the empyrean, or kingdom of fire. Coper- 
nicus made no advance whatever on this idea. Galileo and 
Kepler seem to have made the first real advance — the former 
by resolving the Milky Way into stars with his telescope, the 
latter by suggesting that our sun might be simply one of nu- 
merous stars scattered through space, looking so bright only 
on account of our proximity to it. In the problem of the 
stellar system this conception held the same important place 
which that of the earth as a planet did in the problem of the 
solar system. But Kepler was less fortunate than Copernicus 
in that he failed to commend his idea, even to his own judg- 



LX TROD I '( TOR Y BEMA JiKS. 4 1 7 

ment. It was by affording a starting-point for the researches 

of Kant and Ilerschel that Kepler's suggestion really bore 
fruit. 

Notwithstanding the amount of careful research which 
Ilerschel and his successors have devoted to it, we are still 
very far from having reached even an approximate solution 
of the problem of which we speak. In whatever direction we 
pursue it, we soon find ourselves brought face to face with the 
infinite in space and time. Especially is this the case when 
we seek to know, not simply what the universe is to-day. but 
what causes are modifying it from age to age. All the knowl- 
edge that man has yet gathered is then found to amount to 
nothing but some faint glimmers of li^ht shining here and 
there through the seemingly boundless darkness. The glim- 
mer is a little brighter for each successive generation, but 
many centuries must elapse before we can do much more 
than tell how the nearer stars are situated in space. Indeed, 
we see as yet but little hope that an inhabitant of this planet 
will ever, from his own observations and those of his prede- 
cessors, be able to completely penetrate the mystery in which 
the structure and destiny of the cosmos are now enshrouded. 
However this may be in the future, all we can do at present 
is to form more or less probable conjectures, founded on all 
we know of the general character of natural law. In a strictly 
scientific treatise, such conjectures Mould rind no place ; and 
if we had to grope in absolute darkness, they would be en- 
tirely inappropriate in any but a poetical or religious produc- 
tion. But the subject is too fascinating to permit us to neg- 
lect the faintest light by the aid of which we may penetrate 
the mystery ; we shall therefore briefly set forth both what 
men of the past have thought on the subject, what the science 
of to day enables us to assert with some degree of probability, 
and what knowledge it wholly denies us. To proceed in sci- 
entific order, we must commence by laying a wide foundation 
of facts. Our first step will therefore be to describe the heav- 
ens as they appear to the naked eye, and as they are seen in 
the telescope. 



4:18 THE STELLAR UNIVERSE. 



CHAPTER I. 

THE STARS AS THEY AEE SEEN. 

§ 1. Number and Orders of Stars and Nebulae. 

The total number of stars in the celestial sphere visible 
with the average naked eve may be estimated, in round num- 
bers, as 5000. The number varies so much with the perfec- 
tion and training of the eye, and with the atmospheric condi- 
tions, that it cannot be stated very definitely. When the tele- 
scope is pointed at the heavens, it is found that for every star 
visible to the naked eye there are hundreds, or even thousands, 
too minute to be seen without artificial aid. From the counts 
of stars made by Herschel, Struve has estimated that the total 
number of stars visible with Herschel's twenty-foot telescope 
was about 20,000,000. The great telescopes of modern times 
would, no doubt, show a yet larger number ; but a reliable 
estimate has not been made. The number is probably some- 
where between 30,000,000 and 50,000,000. 

At a very early age, the stars were classified according to 
their apparent brightness or magnitude. The fifteen brightest 
ones were said to be of the first magnitude ; the fifty next in 
order were termed of the second magnitude, and so on to the 
sixth, which comprised the faintest stars visible to the naked 
eye. The number of stars of each order of magnitude be- 
tween the north pole and the circle 35° south of the equator 
is about as follows : 

Of magnitude 1 there are about 14 stars. 

2 " 48 " 

" 3 " 152 " 

4 " 313 " 

5 " 854 " 

" 6 " 2010 " 



Total visible to naked eve 3391 



NUMBER AND ORDERS OF STARS AND NEBULAE. 41'J 

This limit includes all the stars which, in the Middle States, 
culminate at a greater altitude than 15°. The number of the 
sixth magnitude which can be seen depends very much upon 
the eye of the observer and the state of the sky. The forego- 
ing list includes all that can be seen by an ordinary good eye 
in a clear sky when there is no moonlight; but the German 
astronomer Ileis, from whom these numbers are taken, gives a 
list of 1964 more which he believes he can see without a glass. 

The system of expressing the brightness of the stars by a 
series of numbers is continued to the telescopic stars. The 
smallest star visible with a six-inch telescope under ordinary 
circumstances is commonly rated as of the thirteenth magni- 
tude. On the same scale, the smallest stars visible with the 
largest telescopes of the world would be of about the six- 
teenth magnitude, but no exact scale for these very faint stare 
has been arranged. 

Measures of the relative brilliancy of the stars indicate 
that, as we descend in the scale of magnitude, the quantity 
of light emitted diminishes in a geometrical ratio, the stars 
of each order being, in general, between two-h'fths and one- 
third as bright as those of the order next above them. This 
order of diminution is not, however, exact, because the arrange- 
ment of magnitudes has been made by mere estimation of in- 
dividual observers who may have hit on different and varying 
ratios; but it is a sufficient approach to the truth for common 
purposes. From the second to the fifth magnitude the dimi- 
nution is probably one -third in each magnitude, after that 
about two-fifths. Supposing the ratio two-fifths to be exact, 
we find that it would take about 

2h stars of the second magnitude to make one of the first. 

6 " third 

16 " fourth 

40 " fifth 

100 " sixth " " " 

10,000 " eleventh " " " 

1,000,000 " sixteenth " " " 

The number of stars of the several scales of magnitude 
vary in a ratio not far different from the inverse of that of 



420 THE STELLAR UNIVERSE. 

their brightness, the ratio being a little greater in the case of 
the higher magnitudes, and probably a little less in the case 
of the lower ones. Thus, we see that there are about three 
times as many stars of the second magnitude as of the first, 
three times as many of the third as of the second, and after 
that something less than three times as many of each magni- 
tude as of the magnitude next above. Comparing this with 
the table of relative brightness just given, we may conclude 
that if all the stars of each magnitude were condensed into a 
single one, the brightness of the combined stars thus formed 
would not vary extravagantly from one to another until we 
had passed beyond the ninth or tenth magnitude. But it is 
certain that the brightness would ultimately diminish, because 
otherwise there would be no limit to the total amount of light 
given by the stars, and the whole heavens would shine like 
the sun. 

The reader will, of course, understand that this arrange- 
ment by magnitude is purely artificial. Really the stars are 
of every order of brightness, varying by gradations which are 
entirely insensible, so that it is impossible to distinguish be- 
tween the brightest star of one magnitude and the faintest of 
the magnitude next above it. Hence, those astronomers who 
wish to express magnitudes with the greatest exactness, divide 
them into thirds or even tenths ; so that, for instance, stars be- 
tween the sixth and seventh magnitudes are called 6.1, 6.2, 
6.3, and so on to 6.9, according to their brilliancy. Various 
attempts have been made to place the problem of the relative 
amounts of light emitted by the stars upon a more exact basis 
than this old one of magnitudes, but this is a very difficult 
thing to do, because there is no way of measuring light except 
by estimation with the eye. In order to measure the relative 
intensity of two lights, it is necessary to have some instrument 
by which the intensity of one or both the lights may be varied 
until the two appear to be equal. Instruments for this pur- 
pose are known as photometers, and are of various construc- 
tions. For comparing the light of different stars, the photom- 
eter most used at the present time is that of Zollner. By 



NUMBER AND ORDERS OF STARS AND NEBULuE. 421 

this instrument the light of the stars, as seen through a small 
telescope, is compared both in color and intensity with that of 
an artificial star, the light of which can be varied at pleasure. 
A complete set of measures with this instrument, including 
most of the brighter stars, is one of the wants of astronomy 
which we may soon hope to see supplied. The most extended 
recent series of photometric estimates with which the writer 
is acquainted is that of Professor Seidel, of Munich, which in- 
cludes 209 stars, the smallest of which are of the fifth magni- 
tude. An interesting result of these estimates is that Sinus 
gives ns four times as much light as any other star visible in 
our latitude. 

Catalogues of Stars. — In nearly every age in which astron- 
omy has flourished catalogues of stars have been made, giving 
their positions in the heavens, and the magnitude of each. 
The earliest catalogue which has come to ns is found in the 
"Almagest" of Ptolemy, and is supposed to be that of Hippar- 
chus, who flourished 150 years before the Christian era. It 
is said, but not on the best authority, that he constructed it in 
order that future generations might find whether any change 
had in the mean time taken place in the starry heavens. An 
examination of the catalogue shows that the constellations pre- 
sented much the same aspect two thousand years ago that they 
do now. There are two or three stars of his catalogue which 
cannot now be certainly identified ; but it is probable that the 
difficulty arises from the imperfection of the catalogue, and 
from the errors which may have crept into the numerous 
transcriptions of it during the sixteen centuries which elapsed 
before the art of printing was discovered. The catalogue of 
Hipparchus contains only about 10S0 stars, so that he could 
not have given all that he was able to see. He probably omit- 
ted many stars of the smaller magnitudes. The actual num- 
ber given in the "Almagest"' is still less, being only 1030. 

The next catalogue in the order of time is that of Ulugh 
Beigh, a son of the Tartar monarch Tamerlane, which dates 
from the fifteenth century. For the most part, the stars are 
the same as in the catalogue of Ptolemy, only the places were 



422 THE STELLAR UNIVERSE. 

redetermined from the observations at Samareand. It con- 
tains 1019 stars, eleven less than Ptolemy gives. Tycho Brahe, 
having made so great an improvement in the art of observa- 
tion, very naturally recatalogued the stars, determining their 
positions with yet greater accuracy than his predecessors. His 
catalogue is the third and last important one formed before 
the invention of the telescope. It contains 1005 stars. 

Our modern catalogues may be divided into two classes : 
those in which the position of each star in the celestial sphere 
(right ascension and declination) is given with all attainable 
precision, and those in which it is only given approximately, 
so as to identify the star, or distinguish it from others in its 
neighborhood. The catalogues of the former class are very 
numerous, but the more accurate ones are necessarily incom- 
plete, owing to the great labor of making the most exact de- 
termination of the position of a star. There are, perhaps, 
between ten or twenty thousand stars the positions of which 
are catalogued with astronomical precision, and a hundred 
thousand more in which, though entire precision is aimed at, 
it is not attained. Of the merely approximate catalogues, the 
greatest one is the " Stern verzeichniss " of Argelander, which 
enumerates all the stars down to the ninth magnitude between 
the pole and two degrees south of the equator. The work 
tills three thin quarto volumes, and the entire number of stars 
catalogued in it exceeds three hundred thousand. This " star 
census" is being continued to the south pole at the observa- 
tory of Cordoba, South America, by Dr. Gould. Of the mill- 
ions of stars of the tenth magnitude and upwards, hardly one 
in a thousand is, or can be, individually known or catalogued. 
Except as one or another may exhibit some remarkable pecu- 
liarity, they must pass unnoticed in the crowd. 

Division into Constellations. — A single glance at the heavens 
shows that the stars are not equally scattered over the sky, but 
that great numbers of them, especially of the brighter ones, 
are collected into extremely irregular groups, known as con- 
stellations. At a very early age the heavens were represented 
as painted over with figures of men and animals, so arranged 



NUMBER AND ORDERS OF STARS AND NEBULJE. 42.',' 

as to include the principal stars of each constellation. There 
is no historic record of the time when this was done, nor of the 
principles by which those who did it carried out their work; 
but many of the names indicate that it was during the heroic 
age. Some have sought to connect it with the Argonautic ex- 
pedition, from the fact that several heroes of that expedition 
were among those thus translated to the heavens; but this is 
little more than conjecture. So little pains was taken to fit 
the figures to the constellations that we can hardly suppose 
them to have all been executed at one time, or on any well- 
defined plan. Quite likely, in the case of names of her 
the original object was rather to do honor to the man than to 
serve any useful purpose in astronomy. Whatever their ori- 
gin, these names have been retained to the present day, al- 
though the figures which they originally represented no longer 
serve any astronomical purpose. The constellation Hercules, 
for instance, still exists ; but it no longer represents the figure 
of a man among the stars, but a somewhat irregular portion 
of the heavens, including the space in which the ancients 
placed that figure. In star-maps, designed for school instruc- 
tion and for common use, it is still customary to give these 
figures, but they are not generally found on maps designed 
for the use of astronomers. 

Naming the Stars. — The question how to name the individ- 
ual stars in each constellation, so as to readily distinguish 
them, has always involved some difficulty. In the ancient 
catalogues they were distinguished by the part of the figure 
representing the constellation in which they were found ; as. 
the eye of the Bull, the tail of the Great Bear, the right shoul- 
der of Orion, and so on. The Arabs adopted the plan of giv- 
ing special names to each of the brighter stars, or adopting 
such names from the Greeks. Thus, we have the well-known 
stars Sirius, Arcturus, Procyon, Aldebaran. and so on. Most 
of these names have dropped entirely out of astronomical use, 
though still found on some school maps of the stars. The 
system now most in use for the brighter stars was designed by 
Bayer, of Augsburg, Germany, about 1610. He published a 



424 THE STELLAR UNIVERSE. 

set of star-maps, in which the individual stars of each constel- 
lation were designated by the letters of the Greek alphabet — 
a, j3, y, etc. The first letters were given to the brightest stars, 
the next ones to the next brightest, and so on. After the 
Greek letter is given the Latin name of the constellation in 
the genitive case. Thus, Alpha (a) Scorpii, or Alpha of the 
Scorpion, is the name of Antares, the brightest star in Scor- 
pius ; a Lyrse, of the brightest star in the Lyre ; and so on. 
•We have here a resemblance to our system of naming men, 
the Greek letter corresponding to the Christian name, and the 
constellation to the surname. When the Greek alphabet was 
exhausted, without including all the conspicuous stars, the 
Latin alphabet was drawn upon. 

The Bayer system is still applied to all the stars named by 
him. Most of the other stars down to the fifth magnitude are 
designated by a system of numbers assigned by Flamsteed in 
his catalogue. Yet other stars are distinguished by their num- 
bers in some well-known catalogue. When this method fails, 
owing to the star not being catalogued, the position in the 
heavens must be given. 

The Milky Way, or Galaxy. — To the naked eye so much of 
the Galaxy as can be seen at one time presents the appearance 
of a white, cloud-like arch, resting on two opposite points of 
the horizon, and rising to a greater or less altitude, according 
to the position of the celestial sphere relative to the observer. 
Only half of the entire arch can be seen above the horizon at 
once, the other half being below it, and directly opposite the 
visible half. Indeed, there is a portion of it which can never 
be seen in our latitude, being so near the south pole that it 
is always below our horizon. If the earth were removed, or 
made transparent, so that we could see the whole celestial 
sphere at once, the Galaxy would appear as a complete belt 
extending around it. The telescope shows that the Galaxy 
arises from the light of countless stars, too minute to be sep- 
arately visible with the naked eye. We find, then, that the 
telescopic stars, instead of being divided up into a limited 
number of constellations, are mostly condensed in the region 



DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 425 

of the Galaxy. They are least numerous in the regions most 

distant from the galactic belt, and grow thicker as we ap- 
proach it. The more powerful the telescope, the more marked 
the condensation is. With the naked eye, the condensation is 
hardly noticeable, unless by actual count : a very small tele- 
scope will show a decided thickening of the stars in and near 
the Galaxy; while, if we employ the most powerful telescopes, 
a large majority of the stars they show are found to lie act- 
ually in the Galaxy. In other words, if \v T e should blot out 
all the stars visible with a twelve-inch telescope, we should 
find that the greater part of the remaining stars were in the 
Galaxy. The structure of the universe which this fact seems 
to indicate will be explained in a subsequent section. 

Clusters. — Besides this gradual and regular condensation 
towards the galactic belt, occasional condensations of stars 
into clusters may be seen. Indeed, some of these clusters are 
visible to the naked eye, sometimes as separate stars, like the 
Pleiades, but more commonly as milky patches of light, be- 
cause the stars are too small to be seen separately. The num- 
ber visible in powerful telescopes is, however, much greater. 
Sometimes there are hundreds, or even thousands, of stars visi- 
ble in the field of the telescope at once; and sometimes the 
number is so great, and the individual stars so small, that they 
cannot be counted even in the most powerful telescopes ever 
made. 

Nebulae. — Another class of objects which are found in the 
celestial spaces are irregular masses of soft, cloudy light, 
which are hence termed nebula?. Many objects which look 
like nebulae in small telescopes are found by more powerful 
ones to be really star clusters. But, as we shall hereafter 
show, many of these objects are not composed of stars at all, 
but of immense masses of gaseous matter. 

§ 2. Description of the Principal Constellations. 

For the benefit of the reader who wishes to make himself 
acquainted with the constellations in detail, or to identify any 
bright star or constellation which he may see, we present a 



426 THE STELLAR UNIVERSE. 

brief description of the principal objects which may be seen 
in the heavens at different seasons, illustrated by five maps, 
showing the stars to the fifth magnitude inclusive. The 
reader who does not wish to enter into these details can pass 
to the next section without any break of the continuity of 
thought. 

For the purpose of learning the constellations, the star- 
maps will be a valuable auxiliary. It will be better to begin 
with the northern, or circumpolar, constellations, because these 
are nearly always visible in our latitude. The first one to be 
looked for is Ursa Major (the Great Bear, or the Dipper), from 
which the pole star can always be found by means of the 
pointers, as shown in Fig. 2, page 10. Supposing the observer 
to look for it at nine o'clock in the evening, he will see it in 
various positions, depending on the time of year, namely, in 

April and May north of the zenith. 

July and August to the west of north, the pointers lowest. 

October and November close to the north horizon. 

January and February to the east of north, the pointers highest. 

These successive positions are in the same order with those 
which the constellation occupies in consequence of its diurnal 
motion around the pole. The pointers are in the body of the 
bear, while the row of stars on the other end of the constella- 
tion forms his tail. 

Ursa Minor, or the Little Dipper, is the constellation to 
w T hich the pole star belongs. It includes, besides the pole 
star, another star of the second magnitude, which lies nearly 
in the direction of the tail of Ursa Major. 

Cassiopeia, or the Lady in the Chair, is on the opposite side 
of the pole from Ursa Major, at nearly the same distance. 
The constellation can be readily recognized from its three or 
four bright stars, disposed in a line broken into pieces at right 
angles to each other. In the ancient mythology, Cassiopeia is 
the queen of Cepheus ; and in the constellation she is repre- 
sented as seated in a large chair or throne, from which she is 
issuing her edicts. 

Perseus is quite a brilliant constellation, situated in the 



DESCRIPTION OF THE PRINCIPAL C0N8TELLATI0N8. 42 



Milky Way, east" of Cassiopeia, and a little farther from the 
pole. It may be recognized by a row of conspicuous stars 
extending along the Milky Way, which passes directly through 
this constellation. 

Other circnmpolar constellations are Cepheus, the Camelo- 
pard, the Lynx, the Dragon (Draco), and the Lizard ; but they 
do not contain any stars so bright as to attract especial atten- 
tion. The reader who wishes to learn them can easily find 
them by comparing the star-maps with the heavens. 

Owing to the annual motion of the sun among the stars, the 
constellations which are more distant from the pole cannot be 
seen at all times, but must be looked for at certain season-, 
unless inconvenient hours of the night be chosen. We shall 
describe the more remarkable constellations as they are seen 
by an observer in middle north latitudes in four different 
positions of the starry sphere. The sphere takes all four of 
these positions every day, by its diurnal motion; but some of 
these positions will occur in the daytime, and others late at 
night or early in the morning. 

First Position, Orion on tlte Meridian.- — The constellations 
south of the zenith are those shown on Maps II. and III., the 
former being west of the meridian, the latter east. This posi- 
tion occurs on 

December 21st at midnight 

January 21st at 10 o'clock p.m. 

February 20th at 8 o'clock p.m. 

March 21st at 6 o'clock p.m. 

And so on through the year. In this position. Cassiopeia and 
Ursa Major are near the same altitude, the former high up in 

* In the celestial sphere the points of the compass have, of necessity, a mean- 
ing which may seem different from that which we attribute to them on the earth. 
North always means towards the north pole; south, from it: icest, in the direc- 
tion of the diurnal motion : east, in the opposite direction. In Fig. 2, the arrows 
all point west, and by examining the figure it will be seen that below the pole 
north is upwards, and east is towards the west horizon. Eeally, these definitions 
hold equally true for the earth, the same differences being found between the 
points of the compass at different places on the earth — here and in China, for in- 
stance — that we see on the celestial sphere. 



428 THE STELLAR UNIVERSE. 

the north-west, the latter in the north-east. The Milky Way 
spans the heavens like an arch, resting on the horizon in the 
north-north-west and south-south-east. We shall first describe 
the constellations in its course. 

Qygnus, the Swan, is sinking below the horizon, where the 
Milky Way rests upon it in the north-north-west, and only a 
few stars of it are visible. It will be better seen at another 
season. 

Next in order come Cepheus, Cassiopeia, and Perseus, which 
we have already described as circumpolar constellations. 

Above Perseus lies Auriga, the Charioteer, which may be 
readily recognized by a bright star of the first magnitude, 
called Capella, the Goat, now a few degrees north-west of the 
zenith. Auriga is represented as holding a goat in his arm, 
in the body of which this star is situated. About ten degrees 
east of Capella is the star j3 Aurigse of the second magnitude ; 
while still farther to the east is a group of small stars which 
also belongs to the same constellation. The latter extends 
some distance south of the zenith. 

The Milky Way next passes between Taurus and Gemini, 
which we will describe presently, and then crosses the equator 
east of Orion, the most brilliant constellation in the heavens, 
having two stars of the first magnitude and four of the second. 
The former are Betelguese, or a Orionis, which is highest up, 
and may be recognized by its reddish color, and Rigel, or /3 
Orionis, a sparkling white star, lower down, and a little to the 
west. The former is in the shoulder of the figure, the latter 
in the foot. Between the two, three stars of the second mag- 
nitude, in a row, form the belt of the warrior. 

Canis Minor, the Little Dog, lies just across the Milky Way 
from Orion, and may be recognized by the bright star Pro- 
cyon, of the first magnitude, due east from Betelguese. 

Canis Major, the Great Dog, lies south-east of Orion, and is 
easily recognized by Sirius, the brightest fixed star in the heav- 
ens. A number of bright stars south and south-east of Sirius 
belong to this constellation, making it one of great brilliancy. 

As the Milky Way approaches the south horizon, it passes 






DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 429 

through Argo Navis, the Ship Argo, which is partly below the 
horizon. It contains Canopus, the next brightest star to Siri- 
us; but this object is below the horizon, unless the observer is 
as far south as 35° of north latitude. 

We can next trace such of the zodiacal constellations as are 
high enough above the horizon. In the west, one-third of the 
way from the horizon to the zenith, will be seen Aries, the 
Rani, which may be recognized by three stars of the second. 
third, and fourth magnitudes, respectively, forming an obtuse- 
angled triangle, the brightest star being the highest. The 
arrangement of these stars, and of some others of the fifth 
magnitude, may be seen by Map II. 

Taurus, the Bull, is next above Aries, and may be recog- 
nized by the Pleiades, or "seven stars," as the group is com- 
monly called. Really there are only six stars in the group 
clearly visible to ordinary eyes, and an eye which is good 
enough to see seven will be likely to see four others, or eleven 
in all. A telescopic view of this group will be given in con- 
nection with the subject of clusters of stars. Another group 
in this constellation is the llvades, the principal stars of which 
are arranged in the form of the letter Y, one extremity of the 
Y being formed by Aldebaran, a red star ranked as of the 
first magnitude, but not so bright as a Ononis. 

Gemini, the Twins, lies east of the Milky Way, and may be 
found on the left side of Map II. and the right of Map III. 
The brightest stars of this constellation are Castor and Pollux. 
or a and |3, which lie twenty or thirty degrees south-east or 
east of the zenith, about one-fourth or one-third of the way 
to the horizon. They are almost due north from Procyon : 
that is, a line drawn from Procyon to the pole star passes be- 
tween them. The constellation extends from Castor and Pol- 
lux some distance south and west to the borders of Orion. 

Cancer, the Crab, lies east of Gemini, but contains no bright 
star. The most noteworthy object within its borders is Prae- 
sepe, a group of stars too small to be seen singly, which ap- 
pears as a spot of milky light. To see it well, the night must 
be perfectly clear, and the moon not in the neighborhood. 



430 THE STELLAR UNLYERSE. 

Leo, the Lion, contains the bright star Regulus, about two 
hours above the eastern horizon. This star, with five or six 
smaller ones, forms a sickle, Regulus being the handle. The 
sickle is represented as in the breast, neck, and head of the 
lion, his tail extending nearly to the horizon, where it ends at 
the star Denebola, now just risen. 

Such are the principal constellations visible in the supposed 
position of the celestial sphere. If the hour of observation is 
different from that supposed, the positions of the constellations 
will be different by the amount of diurnal rotation during the 
interval. For instance, if, in the middle of March, we study 
the heavens at eight o'clock instead of six, the western stars 
will be nearer the horizon, the southern ones farther west, and 
the eastern ones higher up than we have described them. 

Second Position of the Celestial Sphere. — The meridian in 
twelve hours of right ascension, near the left-hand edge of 
Map III., and the right-hand edge of Map IY. The stars on 
Map III. are west of the meridian, those of Map IY. east of it. 
This position occurs on 

March 21st at midnight. 

April 20th at 10 o'clock. 

May 21st at 8 o'clock. 

In this position Ursa Major is near the zenith, and Cassiopeia 
in the north horizon. The Milky Way is too near the horizon 
to be visible ; Orion has set in the west ; and there are no very 
conspicuous constellations in the south. Castor and Pollux are 
visible in the north-west, at a considerable altitude, and Pro- 
cyon in the w T est, about an hour and a half above the horizon. 
Leo is west of the meridian, extending nearly to it, while three 
new zodiacal constellations have come into sight in the east. 

Virgo, the Yirgin, has a single bright star — Spica — about 
the brilliancy of Regnlus, now about one hour east of the me- 
ridian, and a little more than half-way from the zenith to the 
horizon. 

Libra, the Balance, has no stars which will attract attention. 
The constellation may be recognized by its position between 
Yirgo and Scorpius. 



DESCRIPTION OF THE PRINCIPAL CONSTELLATIONS. 431 

Scorpius f the Scorpion, is just rising in the south-east, and is 
not yet high enough to be well seen. 

Among the constellations north of the zodiac we have : 

Coma Berenices, the Hair of Berenice, now exactly on the 
meridian, and about ten degrees south of the zenith. It is a 
close, irregular group of very small stars, quite different from 
anything else in the heavens. In the ancient mythology, Ber- 
enice had vowed her hair to the goddess Venus; but Jupiter 
carried it away from the temple in which it was deposited, 
and made it into a constellation. 

Bootes, the Bear-keeper, is a large constellation east of Coma. 
It is marked by Arcturus, a very bright but somewhat red 
star, an hour and a half east of Coma Berenices. 
, Canes Venatici, the Hunting Dogs, are north of Coma. They 
are held in a leash by Bootes, and are chasing [Jrsa Major 
round the pole. 

Corona Borealis, the Northern Crown, lies next east of Bootee 
in the north-east. It is principally composed of ;i pretty semi- 
circle of stars, supposed to form a chaplet, or crown. 

Third Position of the Sphere. — The southern constellations 
are those shown on Maps IV. and V., those of Map IV. being 
west of the meridian, and those of Map V. east of it. This 
position occurs on 

June 21st at midnight 

July 21st at 10 o'clock. 

August 21st at 8 o'clock. 

etc etc. 

In this position the Milky Way is once more in sight, and 
seems to span the heavens, but we do not see the same part 
of it which was visible in the first position. Cassiopeia is 
now in the north-east, and Ursa Major has passed over to the 
north-west. Arcturus is two or three hours high in the west. 
and Corona is above it, two or three hours west of the zenith. 
Commencing, as in the first position, with the constellations 
which lie along the Milky Way, we start upwards from Cas- 
siopeia, pass Cepheus and Lacerta, neither of which contains 
any striking stars, and then reach 

29 



432 THE STELLAR UNIVERSE. 

Cygnus, the Swan, now north-east from the zenith, which 
may be recognized by four or five stars forming a cross, di- 
rectly in the Milky Way/ The brightest of these stars some- 
what exceeds the brightest ones of Cassiopeia. 

Lyra, the Harp, is west and south-west of Cygnus, and near 
the zenith. It contains the bright star Vega, or a Lyrse, of 
the first magnitude, of a brilliant white color with a tinge of 
blue. 

Passing south, over Vulpecula, the Little Fox, and Sagitta, 
the Arrow, the next striking constellation we reach is 

Aquila, the Eagle, now midway between the zenith and the 
horizon, and two hours east of the meridian. It contains a 
bright star — Altair, or a Aquilse — situated between two 
smaller ones, the row of three stars running nearly north and? 
south. 

We next pass west of the Milky Way, and direct our atten- 
tion to a point two hours west of the meridian, and some dis- 
tance towards the south horizon. Here we find 

Scorpius, the Scorpion, a zodiacal constellation and a quite 
brilliant one, containing Antares, or a Scorpii, a reddish star 
of nearly the first magnitude, with a smaller star on each side 
of it, and a long curved row of stars to the west. 

Sagittarius, the Archer, comprises a large collection of sec- 
ond-magnitude stars east of Scorpius, and in and east of the 
Milky Way, and now extending from the meridian to a point 
two hours east of it. 

Capricornus, the Goat, another zodiacal constellation, is now 
in the south-east, but contains no striking stars. The same 
remark applies to Aquarius, the Water-bearer, which has just 
risen, and Pisces, the Fishes, partly below the eastern horizon. 

Leaving the zodiac again, we find, north of Scorpius and 
west of the Milky Way, a very large pair of constellations, 
called Ophiuchus, the Serpent-bearer, and Serpens, the Serpent. 
Ophiuchus stands with one foot on Scorpius, while his head is 
marked by a star of the second magnitude twelve degrees 
north of the equator, and now on the meridian. It is, there- 
fore, one-third or one-fourth of the way from the zenith to the 



DESCRIPTION OF THE Pit IXC IP AL CONSTELLATIONS. 4:33 



horizon. The Serpent, which he holds in his hands, lies with 
its tail in an opening of the Milky Way, south-west of Aquila. 
while its neck and head are formed by a collection of stars of 
the second, third, and fourth magnitudes some distance north 
of Scorpius, and extending up to the borders of Bootes. 

Hercules is a very large constellation, bounded by Corona 
on the west, Lyra on the east, Ophiuchus on the south, and 
Draco on the north. It is now in the zenith, but contains no 
striking stars. 

Draco, the Dragon, lies with his head just north of Hercules, 
while his body is marked by a Ions: curved row of stars ex- 
tending round the pole between the Great and the Little Bear. 
His head is readily recognized by a collection of stars of the 
second and third magnitudes which might well suggest such 
an object. 

Fourth Position of the Sphere. — The southern constellations 
are now found on Maps V. and II. — those of Map V. west of 
the meridian, those of Map II. east of it. The times are : 

September 21st at midnight. 

October 21st at LO o'clock. 

November 20th at 8 < "'clock. 

December 21st at G o'clock. 

In this position Cassiopeia is just north of the zenith, while 
Ursa Major is glimmering in the north horizon. Following 
the Milky Way from Cassiopeia towards the west, we shall 
cross Cepheus, Cygnus, Lyra, and Aquila, while towards the 
east we pass Perseus and Auriga, all of which have been de- 
scribed. 

In the sou tli, the principal constellation is Pegasus, the Fly- 
ing Horse, distinguished by four stars of the second magni- 
tude, which form a large square, each side of which is about 
fourteen degrees. 

Andromeda, her hands in chains, is readily found by a row 
of three bright stars extending north-east from the north-east 
corner of Pegasus in the direction of Perseus. 

Cetus, the Whale, is a large constellation in the south, ex- 
tending from the meridian to a point three hours east of it. 



434 THE STELLAR VNIVEESE. 

Its brightest stars are j3 Ceti, now near the meridian, at an al- 
titude of 20°, which stands by itself, and a Ceti, about 20° be- 
low Aries, which is now about 30° south-east from the zenith. 
The reader who wishes to consult the constellations in 
greater detail can readily do so by means of the star-maps. 

§ 3. New and Variable Stars. 

The large majority of stars always appear to be of the same 
brightness, though it is quite possible that, if the quantity of 
light emitted by a star could be measured with entire preci- 
sion, it would be found in all cases to vary slightly, from time 
to time. There are, however, quite a number of stars in which 
the variation is so decided that it has been detected by com- 
paring their apparent brightness with that of other stars at dif- 
ferent times. More than a hundred such stars are now known ; 
but in a large majority of cases the variation is so slight that 
only careful observation with a practised eye can perceive it. 
There are, however, two stars in which it is so decided that 
the most casual observer has only to look at the proper times, 
in order to see it. These are j3 Persei and o Ceti, or Algol 
and Mira, to which we might add rj Argus, a star of the south- 
ern hemisphere, which exhibits variations of a very striking 
character. 

Variations of Algol. — This star, marked j3 in the constel- 
lation Perseus, may be readily found on Maps I. and II., in 
right ascension 3 hours and declination 40° 23'. When once 
found, it is readily recognized by its position nearly in a line 
between two smaller stars. The most favorable seasons for 
seeing it in the early evening are the autumn, winter, and 
spring. In autumn it will, after sunset, generally be low 
down in the north-east ; in winter, high up in the north, not 
far from the zenith; and in spring, low down in the north- 
west. Usually it shines as a faint second-magnitude star : on 
an accurate scale the magnitude is -about 2 J. But at inter- 
vals of a little less than three days, it fades out to the fourth 
magnitude for a few hours, and then resumes its usual splen- 
dor once more. These changes were first noticed about two 



NEW AND VARIABLE STABS. 4:J0 

centuries ago, but it was not till 1782 that they were accu- 
rately observed. The period is now known to be 2 day.-. 20 
hours, 49 minutes — that is, 3 hours 11 minutes less than three 
days. It takes about four hours and a half to fade away to 
its least brilliancy, and four hours more are spent in recover- 
ing its light; so that there are nine and a half hour.-, during 
each period in which its light is below the average. But near 
the beginning and end of the variations, the change is very 
slow, so that there are not more than five or six horn's during 
which the ordinary eye would see that the star was any smaller 
than usual. 

The apparent regularity of this variation of light at first 
suggested, as an explanation of its cause, that a large dark 
planet was revolving round Algol, and passed over its face 
at every revolution, thus cutting off a portion of its light. 
This theory accounts very well for the salient features of 
the variation. But when the latter came to be studied more 
closely and carefully, it was found that there were small irreg- 
ularities in the variation which the theory would not well ac- 
count for. The period of the variation was found to chang 
little at different times, while the star does not lose and recover 
its light in the same time as it would if the passage of a dark 
body caused the changes. 

Another remarkable variable star, but of an entirely differ- 
ent type, is o Ceti, or Mira (the Wonderful). It may be found 
on Map II., in right ascension 2 hours 12 minutes, declination 
3° 39' south. During most of the time this star is entirely 
invisible to the naked eye, but at intervals of about eleven 
months it shines forth with the brilliancy of a star of the sec- 
ond or third magnitude. It is, on the average, about forty 
days from the time it first becomes visible until it attains its 
greatest brightness, and it then requires about two months to 
become invisible ; so that it comes into sight more rapidly 
than it fades away. It is expected to attain its greatest brill- 
iancy in November, IS 77 ; in October, 1878, and so on, about 
a month earlier each year; but the period is quite irregular, 
ranging from ten ' to twelve months, so that the times of its 



436 THE STELLAR UNIVERSE. 

appearance cannot be predicted with certainty. Its maximum 
brilliancy is also variable, being sometimes of the second mag- 
nitude, and at others only of the third or fourth. 

7] Argus. — Perhaps the most extraordinary known variable 
star in the heavens is >j Argus, of the southern hemisphere, of 
which the position is, right ascension, 10 hours 40 minutes ; 
declination, 59° V south. Being so far south of the equator, 
it cannot be seen in our latitudes, and the discovery and ob- 
servations of the variations of its light have been generally 
made by astronomers who have visited the southern hemi- 
sphere. In 1677, Halley, while at St. Helena, found it to be 
of the fourth magnitude. In 1751, Lacaille found that it had 
increased to the second magnitude. From 1828 to 1838 it 
ranged between the first and second magnitudes. The first 
careful observations of its variability were made by Sir John 
Herschel while at the Cape of Good Hope. He says: "It 
was on the 16th December, 1837, that, resuming the photo- 
metrical comparisons, my astonishment was excited by the ap- 
pearance of a new candidate for distinction among the very 
brightest stars of the first magnitude in a part of the heav- 
ens with which, being perfectly familiar, I was certain that no 
such brilliant object had before been seen. After a momen- 
tary hesitation, the natural consequence of a phenomenon so 
utterly unexpected, and referring to a map for its configura- 
tion with other conspicuous stars in the neighborhood, I be- 
came satisfied of its identity with my old acquaintance, rf Ar- 
gus. Its light, was, however, nearly tripled. While yet low, 
it equalled Rigel, and, when it attained some altitude, was 
decidedly greater."* Sir John states that it continued to in- 
crease until January 2d, 1838, when it was nearly matched 
with a Centauri. It then faded a little till the close of his 
observations in April following, but was still as bright as Al- 
debaran. But in 1842 and 1843 it blazed up brighter than 
ever, and in March of the latter year was second only to 
Sirius. During the twenty-five years following, it slowly but 

* "Astronomical Observations at the Cape of Good Hope," p. 33. 



NEW AND VARIABLE STARS. 437 

steadily diminished : in 1867 it was barely risible to the naked 
eye, and the year following it vanished entirely from the mi- 
assisted view, and has not yet begun to recover its brightness. 

When we speak of this star as the most remarkable of the 
well-known variables, we refer, not to the mere range of its 
variations, but to its brilliancy when at its maximum. Sev- 
eral cases of equally great variation are known ; but the stars 
are not so bright, and therefore would not excite so much no- 
tice. Thus, the star R Andromedae varies from the sixth to 
the thirteenth magnitude in a pretty regular period of 405 
days. When at its brightest, it is just visible to the naked 
eye, while only a large telescope will show it when at Its min- 
imum. A. number of others range through five or six orders 
of magnitude, but o ( leti is the only one of these which ever 
becomes as bright as the second magnitude. 

The foregoing stars are the only ones the variations of 
which would strike the ordinary observer. Among the hun- 
dred remaining ones which astronomers have noticed, (3 Lyrae 
is remarkable for having two maxima and two minima of un- 
equal brilliancy. If we take it when at its greatest minimum. 
we find its magnitude to be -44. In the course of three days, 
it will rise to magnitude 3^. In the course of the week fol- 
lowing, it will first fall t<> the fourth magnitude, and inert 
again to magnitude 3£. In three days more it will drop 
again to its minimum of magnitude 44; the period in which 
it goes through all its changes being thirteen days. This pe- 
riod is constantly increasing. The changes of this star can 
best be seen by comparing it with its neighbor, y Lyrse. Some- 
times it will appear equally bright with the latter, and at other 
times a magnitude smaller." 

* In 187.5, Professor Schonfeld, now director of the observatory at Bonn, pub- 
lished a complete catalogue of known variable stars, the total number being 143. 
The following are the more remarkable ones of his list. The positions are re- 
ferred to the ecliptic and equinox of 187.") : 

T Cassiopeia 1 : right ascension. hours 16 minutes 29 seconds: declination, 55° 
ti'.O N. — This is a case in which a star, having once been observed, was after- 
wards found to be missing. Examination showed that it had so far diminished 
as to be no longer visible without a larger telescope, and continued observations 



438 THE STELLAR UNIVERSE. 

New Stars. — It was once supposed to be no uncommon occur- 
rence for new stars to come into existence and old ones to dis- 
appear, the former being looked upon as new creations, and 
the disappearances as due to the destruction or annihilation 
of those stars, which had fulfilled their end in the economy of 
nature. The supposed disappearances of stars are, however, 
found to have no certain foundation in fact, probably owing 
their origin to errors in recording the position of stars actu- 
ally existing. It was explained, in treating of Practical As- 
tronomy, that the astronomer determines the position of a 
body in the celestial vault by observing the clock-time at which 
it passes the meridian, and the position of the circle of his in- 



showed it to range from the seventh to the eleventh magnitude with a regular 
period of 436 days. 

B Cassiopeia? : right ascension, hours 17 minutes 52 seconds ; declination, 
63° 27'. N. — This is supposed to be the celebrated star which blazed out in 
November, 1572, and was so fully described by Tycho Brahe. But the proof of 
identity can hardly be considered conclusive, especially as no variation has, of re- 
cent years, been noticed in the star. 

o Ceti : right ascension, 2 hours 13 minutes 1 second; declination, 3° 32'. 7 
S. — We have already described the variations of this star. 

j8 Persei, or Algol : right ascension, 3 hours minutes 2 seconds ; declina- 
tion, 40° 28'. 4 N. — The variations of this star, which is the most regular one 
known, have just been described. 

R Auriga?: right ascension, 5 hours 7 minutes 12 seconds; declinntion, 53° 
26'. 6 N. — This star is one of very wide and complex variation, changing from the 
sixth to the thirteenth magnitude in a period of about 465 days. 

R Geminorum : right ascension, 6 hours 59 minutes 49 seconds; declination, 
22° 53'.8 N. — This star was discovered by Mr. Hind, of England, and ranges be- 
tween the seventh and the twelfth magnitude in a period of 371 days. 

U Geminorum: right ascension, 7 hours 47 minutes 41 seconds; declination, 
22° 19'. 7 N. — An irregular variable, never visible to the naked eye, remarkable 
for the rapidity with which it sometimes changes. Schonfeld says that in Feb- 
ruary, 1869, it increased three entire magnitudes in 24 hours. The periods of its 
greatest brightness have ranged from 75 to 617 days. 

t] Argus : right ascension, 10 hours 40 minutes 13 seconds ; declination, 59° 
1'.6 S. — This remarkable object has already been described. 

R Hydras: right ascension. 13 hours 22 minutes 53 seconds; declination, 22° 
38'. S. — The variability of this star was recognized by Maraldi, in 1704. It is 
generally invisible to the naked eye, but rises to about the fifth magnitude at 
intervals of about 437 days. Its period seems to be diminishing, having been 
about 500 days when first discovered. 



NEW AND VARIABLE 8TAB8. 439 

strument when his telescope is pointed at the ohject. If he 
happens to make a mistake in writing down any of tl 
numbers — if, for example, he gets his clock-time one minute 
or five minutes wrong, or puts down a wrong number of de- 
grees for the position of his circle — he will write down the 
position of the star where none really exists. Then, some sub- 
sequent astronomer, looking in this place and seeing no star, 
may think the star has disappeared, when, in reality, there was 
never any star there. Where thousands of numbers have to be 
written down, such mistakes will sometimes occur; and it is to 
them that some cases of supposed di>appearance of stars are to 
be attributed. There have, however, been several cases of ap- 
parently new stars coming suddenly into view, of which we 
shall describe some of the most remarkable. 

T Coronaa: right ascension, 15 hours .~>4 minutes 1G seconds; declination, 26° 
lG'.f> N. — This is the "new star" which blazed out in the Northern Crown in 
18GG, as hereafter described. Of late years it has remained between the ninth 
and tenth magnitudes without exhibiting any remarkable variations. 

TScorpii: right ascension; 16 hoars '.» minutes 36 seconds; declination. 22° 
40'.0 S. — This star was discovered by Auwers. in 1860, in the midst of a well- 
known cluster. It gradually diminished daring the following months, and finally 
disappeared entirely among the stars by which it is surrounded. 

— Serpen tari i : right ascension, 17 hours 23 minutes 9 seconds; declination. 
21° 22'. 4 S. — This is supposed to be the celebrated "new star" seen and de- 
scribed by Kepler in 1604, soon to be described. 

X Cygni: right ascension, 19 hours 45 minutes 46 seconds; declination, 32 r 36\0 
N. — This star becomes visible to the naked eye at intervals of about 406 days, and 
then sinks to the twelfth or thirteenth magnitude, so that only large telescopes will 
show it. Its greatest brightness ranges from the fourth to the sixth magnitude. 

i) Aquilre : right ascension, 19 hours 4(5 minutes 6 seconds ; declination. D 
41'. 2 X. — This star varies from magnitude 3? to 4f, and is therefore one of 
those which can readily be observed with the naked eye. Its period is 7 days 4 
hours 14 minutes 4 seconds. 

P Cygni: right ascension, 20 hours 13 minutes 11 seconds; declination, 37° 
38'. 7 N. — This was supposed to be a new star in 1600, when it was first seen 
by Janson. During the remainder of the century it varied from the third to the 
sixth magnitude; but dining two centuries which have since elapsed no further 
variations have been noticed, the star being constantly of the fifth magnitude. 

ft Cephei : right ascension, 21 hours 39 minutes 41 seconds: declination. a8° 
12'.4 N. — One of the reddest stars visible to the naked eye in the northern hemi- 
sphere. Its magnitude is found to vary from the fourth to the fifth in a very ir- 
regular manner. 



440 THE STELLAR UNIVERSE. 

In 1572 an apparently new star showed itself in Cassiopeia. 
It was first seen by Tycho Brahe on November 11th, when 
it had attained the first magnitude. It increased rapidly in 
brilliancy, soon becoming equal to Venus, so that good eyes 
could discern it in full daylight. In December it began to 
grow smaller, and continued gradually to fade away until the 
following May, when it disappeared entirely. This was forty 
years before the invention of the telescope. Tycho has left us 
an extended treatise on this most remarkable star. 

In 1604 a similar phenomenon was seen in the constella- 
tion Ophiuchus. The star was first noticed in October of that 
year, when it had attained the first magnitude. In the follow- 
ing winter it began to wane, but remained visible during the 
whole year 1605. Early in 1606 it faded away entirely, hav- 
ing been visible for more than a year. A very full history of 
this star has been left to us by Kepler. 

The most striking recent case of this kind was in May, 
1866, when a star of the second magnitude suddenly appeared 
in Corona Borealis. On the 11th and 12th of that month it 
was remarked independently by at least five observers in Eu- 
rope and America, one of the first being Mr. Farquhar, of the 
United States Patent-office. Whether it really blazed out as 
suddenly as this would indicate has not been definitively set- 
tled. If, as would seem most probable, it was several days 
attaining its greatest brilliancy, then the only person known 
to have seen it was Mr. Benjamin Hallowell, a well-known 
teacher near Washington, whose testimony is of such a nature 
that it is hard to doubt that the star was visible several days 
before it was generally known. On the other hand, Schmidt, 
of Athens, asserts in the most positive manner that the star 
was not there on May 10th, because he was then scanning 
that part of the heavens, and would certainly have noticed it. 
However the fact may have been in this particular case, it is 
noteworthy that none of the new stars we have described were 
noticed until they had nearly or quite attained their greatest 
brilliancy, a fact which gives color to the view that they have 
all blazed up with great rapidity. 



NEW AXD VARIABLE STARS. 4:4:1 

In November, 1876, a new star of the third magnitude was 
noticed by Schmidt, of Athens, in the constellation Cygnus. 
It soon began to fade away, and disappeared from the unaided 
vision in a few w r eeks. The position of the constellation Cyg- 
nus becomes so unfavorable for observation in November that 
very few people got a sight of this object. 

The view that these bodies may be new creations, designed 
to rank permanently among their fellow-stars, is completely 
refuted by their transient character, if by nothing else. Their 
apparently ephemeral existence is in striking contrast to the 
permanency of the stars in general, which endure from age to 
age without any change whatever. They are now classified 
by astronomers among the variable stars, their changes being 
of a very irregular and fitful character. There is no serious 
doubt that they were all in the heavens as very small stars 
before they blazed forth in this extraordinary manner, and 
that they are in the same place yet. The position of the star 
of 1572 was carefully determined by Tycho Brahe; and a 
small telescopic star now exists within 1' of the place com- 
puted from his observations, and is probably the same. The 
star of 1866 was found to have been recorded as one of the 
ninth magnitude in Ajgelander's great catalogue of the stars 
of the northern hemisphere, completed several years before. 
After blazing up in the way we have described, it gradually 
faded away to its former insignificance, and has shown no 
further signs of breaking forth again. There is a wide differ- 
ence between these irregular variations, or breaking-forth of 
light, on a single occasion in the course of centuries, and the 
regular changes of Algol and )3 Lyras. But the careful obser- 
vations of the industrious astronomers who have devoted them- 
selves to this subject have resulted in the discovery of stars 
of nearly every degree of irregulaiitv between these extremes. 
Some of them change gradually from one magnitude to another, 
in the course of years, without seeming to follow any law what- 
ever, while in others some tendency to regularity can be faintly 
traced. The best connecting link between new and variable stars 
is, perhaps, afforded by ?/ Argus, which we have just described. 



442 THE STELLAR UNIVERSE. 

It is probable that the variations of light of which we have 
spoken are the result of operations going on in the star itself, 
which, it must be remembered, is a body of the same order of 
magnitude and brilliancy with our sun, and that these opera- 
tions are analogous to those which produce the solar spots. It 
was shown in the chapter on the sun that the frequency of 
solar spots shows a period of eleven years, during one portion 
of which there are frequently no spots at all to be seen, while 
during another portion they are very numerous. Hence, if 
an observer so far away in the stellar places as to see our sun 
like a star, could, from time to time, make exact measures of 
the amount of light it emitted, he would find it to be a vari- 
able star, with a period of eleven years, the amount of light 
being least when we see most spots, and greatest when there 
are few spots. The variation would, indeed, be so slight that 
we could not perceive it with any photometric means which 
we possess, but it would exist nevertheless. Now, the general 
analogies of the universe, as well as the testimony of the spec- 
troscope, lead us to believe that the physical constitution of 
the sun and the stars is of the same generalnature. We may 
therefore expect that, as we see spots on the sun which vary 
in form, size, and number from day to day, so, if we could 
take a sufficiently close view of the faces of the stars, we 
should, at least in some of them, see similar spots. It is also 
likely that, owing to the varying physical constitution of these 
bodies, the number and extent of the spots might be found to 
be very different in different stars. In the cases in which the 
spots covered the larger portion of the surface, their variations 
in number and extent would alone cause the star to vary in 
light, from time to time. Finally, we have only to suppose 
the same kind of regularity which we see in the eleven-year 
cycle of the solar spots, to have a variation in the brightness 
of a star going through a regular cycle, as in the case of Algol 
and Mira Ceti. 

The occasional outbursts of stars which we have described, 
in which their light is rapidly increased a hundred-fold, would 
seem not to be accounted for on the spot theory, without car- 



NEW AND VARIABLE STABS. 443 

rying this theory to an extreme. It would, in fact, if not 
modified, imply that ninety-nine parts of the surface out of a 
hundred were ordinarily covered with spots, and that on rare 
occasions these spots all disappeared. But the spectroscopic 
observations of the star of 1866 showed an analogy of a little 
different character with operations going on in our sun. Mr. 
Iluggins found the spectrum of this star to be a continuous 
one, crossed by bright lines, the position of which indicated 
that they proceeded partly or wholly from glowing hydrogen. 
The continuous spectrum was also crossed by dark absorption 
lines, indicating that the light had passed through an atmos- 
phere of comparatively cool gas. Mr. Ilnggins's interpreta- 
tion of this is that there was a sudden and extraordinary out- 
burst of hydrogen gas from the star which, by its own light, 
as well as by heating up the whole surface of the star, caused 
the immense accession of brilliancy. Now, we have shown 
that the red flames seen around the sun during a total eclipse 
are caused by eruptions of hydrogen from his interior; more- 
over, these eruptions are generally connected with faculae, or 
portions of the sun's disk several times more brilliant than the 
rest of the photosphere. Hence, it is not unlikely that the 
blazing-forth of this star arose from an action similar to that 
which produces the solar flames, only on an immensely larger 
scale. 

We have thus in the spots, facula?, and protuberances of 
the sun a few suggestions as to what is probably going on in 
those stars which exhibit the extraordinary changes of light 
which we have described. Is there any possibility that our 
sun may be subject to such outbursts of light and heat as 
those we have described in the cases of apparently new and 
temporary stars ? We may almost say that the continued ex- 
istence of the human race is involved in this question ; for if 
the heat of the sun should, even for a few days only, be in- 
creased a hundred-fold, the higher orders of animal and veg- 
etable life would be destroyed. We can only reply to it that 
the general analogies of nature lead us to believe that we 
need not feel any apprehension of such a catastrophe. Not 



444 THE STELLAR UNIVERSE. 

the slightest certain variation of the solar heat has been de- 
tected since the invention of the thermometer, and the gen- 
eral constancy of the light emitted by ninety-nine stars out of 
every hundred may inspire us with entire confidence that no 
sudden and destructive variation need be feared in the case 
of our sun. 

§ 4. Double Stars. 

Telescopic examination shows that many stars which seem 
single to the naked eye are really double, or composed of a 
pair of stars lying side by side. There are in the heavens 
several pairs of stars the components of which are so close 
together that, to the naked eye, they seem almost to touch 
each other. One of the easiest and most beautiful of these 
is in Taurus, quite near Aldebaran. Here the two stars l 
Tauri and 2 Tauri are each of the fourth magnitude. An- 
other such pair is a Capricorni, in which the two pairs are un- 
equal. Here an ordinary eye has to look pretty carefully to 
see the smaller star. Yet another pair is c Lyrse, the com- 
ponents of which are so close that only a good eye can dis- 
tinguish them. These pairs, however, are not considered as 
double stars in astronomy, because, although to the naked eye 
they seem so close, yet, when viewed in a telescope of high 
power, they are so wide apart that they cannot be seen at the 
same time. The telescopic double stars are formed of com- 
ponents only a few seconds apart ; indeed, in many cases, only 
a fraction of a second. The large majority of those which 
are catalogued as doubles range from half a second to fifteen 
seconds in distance. When they exceed the latter limit, they 
are no longer objects of special interest, because they may 
be really without any connection, and appear together only 
because they lie in nearly the same straight line from our 
system. 

The most obvious question which suggests itself here is 
whether in any case there is any real connection between the 
two stars of the pair, or whether they do not appear close to- 
gether, simply because they chance to lie on nearly the same 



DOUBLE STARS. 445 

straight line from the earth. That some stars do appear dou- 
ble in this way there is no doubt, and such pairs are called 
"optically double." But notwithstanding the immense num- 
ber of visible stars, the chance of mai^ pairs falling within 
a few seconds of each other is quite small; and the number 
of close double stars is so great as to preclude all possibility 
that they appear together only by chance. If any further 
proof was wanted that the stars of these pairs are really phys- 
ically connected, and therefore close together in reality as well 
as in appearance, it is found in the fact that many of them 
constitute systems in which one revolves round the other, or, 
to speak more exactly, in which each revolves round the cen- 
tre of gravity of the pair. Such pairs are called binary sys- 
tems, to distinguish them from those in which no such revolu- 
tion has been observed. The revolution of these binary 
tenis is generally very slow, requiring many centuries for it> 
accomplishment ; and the slower the motion, the longer it 
will take to perceive and determine it. Generally it has been 
detected by astronomers of one generation comparing their 
observations with those of their predecessors ; for instance, 
when the elder Struve compared his observations with those 
of Herschel, and when Dawes or the younger Struve compared 
with the elder Struve, a great number of pairs were found to 
be binary. As every observer is constantly detecting new 
cases of motion, the number of binary systems known to as- 
tronomers is constantly increasing. 

A brief account of the manner in which these objects are 
measured may not be out of place. For the purpose in ques- 
tion, the eye-piece of the telescope must be provided with a 
" filar micrometer," the important part of which consists of a 
pair of parallel spider-lines, one of which can be moved side- 
ways by a very fine screw, and can thus be made to pass back 
and forth over the other. The exact distance apart of the 
lines can be determined from the position of the screw. The 
w T hole micrometer turns round on an axis parallel to the tel- 
escope, the centre of which is in the centre of the field of 
view. To get the direction of one star from the other, the ob- 



446 



. THE STELLAR UNIVERSE. 



server turns the micrometer round until the spider-lines are 
parallel to the line joining the two stars, as shown in Fig. 98, 
and he then reads the position circle. Knowing what the 
position circle reads w^hen he turns the wires so that the star 
shall run along them by its diurnal motion, the difference of 
the two angles shows the angle which the line joining the 
two stars makes with the celestial parallel. To obtain the 
distance apart of the stars, the observer turns the micrometer 
90° from the position in Fig. 98, and then turns the screw and 
moves the telescope, until each star is bisected by one of the 
wires, as shown in Fig. 99. The position of the wires is then 
interchanged, and the measure is repeated. The mode in 

N 
k 

\ i 




* 



Fig. 99. 



Fig. 100. 



which the direction of one star from another is reckoned is 
this : Imagine a line, SJSf, in Fig. 100, drawn due north from 
the brighter star, and another, SP, drawn through the smaller 
star. Then the angle NSP which these two lines make with 
each other, counted from north towards east, is the position 
angle of the stars, the changes in which show the revolution 
of one star around the other. 

In a few of the binary systems the period is so short that 
a complete revolution, or more, of the two stars round each 
other lias been observed. As a general rale, the pairs which 
have the most rapid motion are very close, and therefore of 
comparatively recent discovery, and difficult to observe. One 
or two are suspected to have a period of less than thirty years, 
but they are very hard to measure. 

Binary Systems of Short Period.— -The following table shows 



DOUBLE STARS. 



447 



the periods of revolution in the ease of those stars which have 
been observed through a complete revolution, or of which the 
periods have been well determined : 



42 Comae 26 years. 

% Herculis 35 " 

Strove, 3121 40 " 

tj Corona 40 " 

Sirius 50 " 

K Caucri 58 " 



£ UrsaB Majoris B3 y< 

r\ Coronae Borealis 07 

a Centauri 77 

^Ophiuchi 92 

\ Ophiuchi !«; 

£ Scorpii 08 



Two or three others are suspected to move very rapidly, but 
they are so very close and difficult that it is only on favora- 
ble occasions that they can be seen to be double. One of 
the most remarkable stars in this list is Sirius, the period of 
which is calculated, not from the observations of the satel- 
lite, but from the motion of Sirius itself. It has long been 
known that the proper motion of this star is subject to cer- 
tain periodic variations ; and, on investigating these varia- 
tions, it was found by Peters and Auwers that they could be 
completely represented by supposing that a satellite was re- 
volving around the planet in a certain orbit. The elements 
of this orbit were all determined except the distance of the 
satellite, which did not admit of determination. Its direction 
could, however, be computed from time to time almost as ac- 
curately as if it were actually seen with the telescope. But, 
before the time of which we speak, no one had ever seen it. 
Indeed, although many observers must have examined Sirius 
from time to time with good telescopes, it is not likely that 
they made a careful search in the predicted direction. 

Such was the state of the question until February, 1862, 
when Messrs. Alvan Clark & Sons, of Cambridgeport, were 
completing their eighteen-inch glass for the Chicago Observa- 
tory. Turning the glass one evening on Sirius, for the pur- 
pose of trying it, the practised eye of the younger Clark soon 
detected something unusual. " Why, father," he exclaimed, 
" the star has a companion !" The father looked, and there 
was a faint companion due east from the bright star, and dis- 
tant about 10". This was exactly the predicted direction for 

30 



44:8 THE STELLAR UNIVERSE. 

that time, though the discoverers knew nothing of it. As the 
news went round the world, all the great telescopes were 
pointed on Sirius, and it was now found that when observers 
knew where the companion was, many telescopes would show 
it. It lay in the exact direction which theory had predicted 
for that time, and it was now observed with the greatest inter- 
est, in order to see whether it was moving in the direction of the 
theoretical satellite. Four years' observation showed that this 
was really the case, so that hardly any doubt could remain that 
this almost invisible object was really the body which, by its at- 
traction and revolution around Sirius, had caused the inequal- 
ity in its motion. At the same time, the correspondence has 
not since proved exact, the observed companion having moved 
about half a degree per annum more rapidly than the theo- 
retical one. This difference, though larger than was expected, 
is probably due to the inevitable errors of the very delicate 
and difficult observations from which the movements of the 
theoretical companion were computed. 

The visibility of this very interesting and difficult object 
depends almost as much on the altitude of Sirius and the state 
of the atmosphere as on the power of the telescope. When 
the images of the stars are very bad, it cannot be seen even 
in the great Washington telescope, while there are cases of its 
being seen under extraordinarily favorable conditions with tel- 
escopes of six inches aperture or less. These favorable condi- 
tions are indicated to the naked eye by the absence of twinkling. 

A case of the same kind, except that the disturbing satellite 
has not been seen, is found in Procyon. Bessel long ago sus-, 
pected that the position of this star was changed by some at- 
tracting body in its neighborhood, but he did not reach a defi- 
nite conclusion on the subject. Auwers, having made a care- 
ful investigation of all the observations since the time of Brad- 
ley, found that the star moved around an invisible centre 1" 
distant, which was probably the centre of gravity of the star 
and an invisible satellite. This satellite has been carefully 
searched for with great telescopes during the last few years, 
but without success. 



CLU8TER8 OF STARS. 449 

Triple and Multiple Shirs. — Besides double stars, groups 
of three or more stars are frequently found. Such objects 
are known as triple, quadruple, etc. They commonly occur 
through one of the stars of a wide pair being itself a close 
double star, and very often the duplicity of the component 
has not been discovered till long after it was known to form 
one star of a pair. For instance, fi Herculis was recognized 
as a double star by Sir W. Ilerschel, the companion star being 
about 30" distant, and much smaller than ;/ itself. In 1856, 
Mr. Alvan Clark, trying one of his glasses upon it, found that 
the small companion was itself double, being composed of two 
nearly equal stai-s, about 1" apart. This close pair proves to 
be a binary system of short period, more than half a revolu- 
tion of the two stars around each other having been made 
since 1S56. Another case of the same kind is y Andromeda', 
which was found by Ilerschel to have a companion about 1<> 
distant, while Struve found this companion to be itself double. 

Many double and multiple stars are interesting objects for 
telescopic examination. We give in the Appendix a list of 
the more interesting or remarkable of them. 

§ 5. Clusters of Stars. 

A very little observation with the telescope will show that 
while the brighter stars are scattered nearly equally over the 
whole celestial vault, this is not the case with the smaller ones. 
A number of stars which it is not possible to estimate are 
found to be aggregated into clusters, in which the separate 
stars are so small and so numerous that, with insufficient tele- 
scopic power, they present the appearance of a mass of eloudy 
light. We find clusters of every degree of aggregation. At 
one extreme we may place the Pleiades, or "seven stars'* 
which form so well-known an object in our winter sky, in 
which, however, only six of the stars are plainly visible to the 
naked eye. There is an old myth that this group originally 
consisted of seven stars, one of which disappeared from the 
heavens, leaving but six. But a very good eye can even now 
see eleven when the air is clear, and the telescope shows from 



450 THE STELLAR UNIVERSE. 

fifty to a hundred more, according to its power. We present a 
view of this group as it appears through a small telescope. 

No absolute dividing-line can be drawn between such wide- 
ly extended groups as the Pleiades and the densest clusters. 




Fm. 101.— Telescopic view of the Pleiades, after Engelmann. The six larger stars are those 
easily seen by ordinary eyes without a telescope, while the four next in size, having 
four rays each, can be seen by very good eyes. About an inch from the upper right- 
hand corner is a pair of small stars which a very keen eye can see as a single star. 

The cluster Prsesepe, in the constellation Cancer (Map III., 
right ascension, 8 hours 20 minutes ; declination, 20° 10' N.), 
is plainly visible to the naked eye on a clear, moonless night, 
as a nebulous mass of light. Examined with a small tele- 



CLUSTERS OF STARS. 451 

scope, it is found to consist of a group of stars, ranging from 
the seventh or eighth magnitude upwards. For examination 
with a small telescope, one of the most beautiful groups is in 
the constellation Perseus (Map I., right ascension, 2 hours 10 
minutes ; declination, 57° N.). It is seen to the best advantage 
with a low magnifying power, between twenty-five and fifty 
times, and may easily be recognized by the naked eye as a 
little patch of light. 

The heavens afford no objects of more interest to the con- 
templative mind than some of these clusters. Many of them 
are so distant that the most powerful telescopes ever made 
show them only as a patch of star-dust, or a mass of light s<> 
faint that the separate stars cannot be distinguished. Their 
distance from ns is such that they are beyond, not only all 
our means of measurement, but all our powers of estimation. 
Minute as they appear, there is nothing that we know of to 
prevent our supposing each of them to be the centre of a 
group of planets as extensive as our own, and each planet t<> 
be as full of inhabitants as this one. AVe may thus think of 
them as little colonies on the outskirts of creation itself, and 
as we see all the suns which give them light condensed into 
one little speck, we might be led to think of the inhabitants 
of the various systems as holding intercourse with each other. 
Yet, were we transported to one of these distant clusters, and 
stationed on a planet circling one of the suns which compose 
it, instead of finding the neighboring suns in close proximity, 
we should only see a firmament of stars around us, such as we 
see from the earth. Probably it would be a brighter firma- 
ment, in which so many stars would glow with more than the 
splendor of Sirius, as to make the night far brighter than 
ours; but the inhabitants of the neighboring worlds would as 
completely elude telescopic vision as the inhabitants of Mars 
do here. Consequently, to the inhabitants of every planet in 
the cluster, the question of the plurality of worlds might be 
as insolvable as it is to us. 

To give the reader an idea what the more distant of these 
star clusters looks like, we present two views from Sir John 



452 



THE STELLAR UNIVERSE. 



Herschel's observations at the Cape of Good Hope. Fig. 102 
shows the cluster numbered 2322 in Herschel's catalogue, and 
known as 47 Toucani. That astronomer describes it as ''a 
most glorious globular cluster, the stars of the fourteenth mag- 
nitude immensely numerous. It is compressed to a blaze of 
light at the centre, the diameter of the more compressed part 
being 30" in right ascension." Fig. 103 is No. 3504 of Her- 
schel : " The noble globular cluster w Centauri, beyond all 
comparison the richest and largest object of the kind in the 
heavens. The stars are literally innumerable, and as their 




North. 

Fig. 102 Cluster 47 Toucani. Eight ascen- 
sion, hours 18 minutes ; declination, 



Fig. 103.— Cluster w Centauri. Right ascen- 
sion, 13 hours 20 minutes ; declination, 
46° 52' S. 



72° 45' S. 

total light when received by the naked eye affects it hardly 
more than a star of the fifth or fourth to fifth magnitude, the 
minuteness of each star may be imagined." 

§ 6. Nebulce. 

Nebulae appear to us as masses of soft diffused light, of 
greater or less extent. Generally these masses are very ir- 
regular in outline, but a few of them are round and well- 
defined. These are termed planetary nebulce. It may some- 
times be impossible to distinguish between star clusters and 
nebulae, because when the power of the telescope is so low 
that the separate stars of a cluster cannot be distinguished, 
they will present the appearance of a nebula. To the naked 
eye the cluster Prsesepe, described in the last chapter, looks 



NEBUL2E. 453 

exactly like a nebula, though a very small telescope will re- 
solve it into stars. The early observers with telescopes de- 
scribed many objects as nebulae which the more powerful in- 
struments of Ilersehel showed to be clusters of stars. Thus 
arose the two classes of resolvable and irresolvable nebula-, 
the first comprising such as could be resolved into stars, and 
the second such as could not. It is evident, from what we 
have just said, that this distinction would depend partly on 
the telescope, since a nebula which was irresolvable in one 
telescope might be resolvable in another telescope of greater- 
power. This suggests the question whether all nebulas may 
not really be clusters of stars, those which are irresolvable ap- 
pearing so merely because their distance is so great that the 
separate stars which compose them cannot be distinguished 
with our most powerful telescopes. If this were so, there 
would be no such thing as a real nebula, and everything 
which appears as such should be classified as* a star cluster. 
The spectroscope, as we shall presently show, has settled this 
question, by showing that many of these objects are immense 
masses of glowing gas, and therefore cannot be stars. 

Classification and Forms of Nebula?. — The one object of this 
class which, more than all others, has occupied the attention 
of astronomers and excited the wonder of observers, is the 
great nebula of Orion. It surrounds the middle of the three 
stars which form the sword of Orion. Its position may be 
found on Maps II. and III., in right ascension 5 hours 28 
minutes, declination 6° S. A good eye will perceive that 
this star, instead of looking like a bright point, as the other 
stars do, has an ill-defined, hazy appearance, due to the sur- 
rounding nebulae. This object was first described by Huy- 
ghens in 1659, as follows : 

" There is one phenomenon among the fixed stars worthy 
of mention which, so far as I know, has hitherto been noticed 
by no one, and indeed cannot be well observed except with 
large telescopes. In the sword of Orion are three stars quite 
close together. In 1656, as I chanced to be viewing the mid- 
dle one of these with the telescope, instead of a single star. 



454: 



THE STELLAR UNIVERSE. 



twelve showed themselves (a not uncommon circumstance). 
Three of these almost touched each other, and, with four oth- 
ers, shone through a nebula, so that the space around them 
seemed far brighter than the rest of the heavens, w T hich was 
entirely clear, and appeared quite black, the effect being that 
of an opening in the sky, through which a brighter region 
was visible."* 




Fig. 104 The great nebula of Orion, as drawn by Trouvelot with the twenty-six-inch 

Washington telescope. 

Since that time it has been studied with large telescopes 
by a great number of observers, including Messier, the two 



* Systema Saturnium, p. 8. The last remark of Huyghens seems to have pro- 
duced the impression that he or some of the early observers considered the nebulae 
to be real openmgs in the firmament, through which they got glimpses of the 
glory of the empyrean. But it may be doubted whether the old ideas of the firma- 
ment and the empyrean were entertained by any astronomer after the invention 
of the telescope, and there is nothing in the remark of Huyghens to indicate that 
he thought the opening really existed. His words are rather obscure. 



NEBULA. 455 

Ilerschels, Rosse, Stnive, and the Bonds. The representation 
which we give in Fig. 104 is from a drawing made by Mr. 
Trouvelot with the great Washington telescope. In brilliancy 
and variety of detail it exceeds any other nebula visible in 
the northern hemisphere. The central point of interest is oc- 
cupied by four comparatively bright stars, easily distinguished 
by a small telescope with a magnifying power of 40 or 50, 
combined with two small ones, requiring a nine-inch telescope 
to be well seen. The whole of these form a sextuple* group. 
included in a space a few seconds square, which alone would 
be an interesting and remarkable object. Besides these, the 
nebula is dotted with so many stars that they would almost 
constitute a cluster by themselves. 

In the winter of 1864-05, the spectrum of this object was 
examined independently by Secchi and Iluggins, who found 
that it consisted of three bright lines, and hence concluded 
that the nebula was composed, not of stars, but of glowing 
gas. The position of one of the lines was near that of a line 
of nitrosren, while another seemed to coincide with a hydrogen 
line. There is, therefore, a certain probability that this object 
is a mixture of hydrogen and nitrogen gas, though this is a 
point on which it is impossible to speak with certainty. 

Another brilliant nebula visible to the naked eve is the 
great one of Andromeda (Maps II. and V., right ascension, 
hours 35 minutes ; declination, 40° N.). The observer can 
see at a glance with the naked eye that this is not a star, but 
a mass of diffused light. Indeed, untrained observers have 
sometimes very naturally mistaken it for a comet.* It was 
first described by Marius, in 1614, who compared its light to 
that of a candle shining through horn. This gives a very 
good idea of the singular impression it produces, which is that 
of an object not self-luminous, but translucent, and illuminated 
by a very brilliant light behind it. With a small telescope, it 

* A ship-captain who had crossed the Atlantic once visited the Cambridge Ob- 
servatory, to tell Professor Bond that he had seen a small comet, which remained 
in sight during his entire voyage. The object proved to be the nebula uf An- 
dromeda. 



456 



THE STELLAR UNIVERSE. 



is easy to imagine it to be a solid like horn ; but with a large 
one, the effect is much more that of a great mass of matter, 
like fog or mist, which scatters and reflects the light of a brill- 
iant body in its midst. That this impression can be correct, 
it would be hazardous to assert ; but the result of a spectrum 




Fio. 105.— The annular nebula in Lyra. Drawn by Professor E. S. Holden. 

analysis of the light of the nebula certainly seems to favor it. 
Unlike most of the nebulae, its spectrum is a continuous one, 
similar to the ordinary spectra from heated bodies, thus indi- 
cating that the light emanates, not from a glowing gas, but 
from matter in the solid or liquid state. This would suggest 



NEBUL&. 457 

the idea that the object is really an immense star- cluster, bo 
distant that the most powerful telescopes cannot resolve it. 
Though we cannot positively deny the possibility of this, yet 
in the most powerful telescopes the light fades away so softly 
and gradually that no such thing as a resolution into stars 
seems possible. Indeed, it looks less resolvable and more like 
a gas in the largest telescopes than in those of moderate size. 
If it is really a gas, and if the spectrum is continuous through- 
out the whole extent of the nebula, it would indicate either 
that it shone by reflected light, or that the gas was subjected 
to a great pressure almost to its outer limit, which hardly seems 
possible. But, granting that the light is reflected, we cannot 
say whether it originates in a single bright star or in a num- 
ber of small ones scattered about through the nebula. 

Another extraordinary object of this class is the annular, or 
ring-nebula of Lyra, situated in that constellation, about half- 
way between the stars /3 and y. In the older telescopes it 
looked like a perfect ring; but the larger ones of modern times 
show that the opening of the ring is really filled with nebu- 
lous light ; in fact, that we have here an object of very regular 
outline, in which the outer portion is brighter than the inte- 
rior. Its form is neither circular nor exactly elliptic, but egg- 
shaped, one end being more pointed than the other. A mod- 
erate-sized telescope will show it, but a large one is recpiired 
to see it to good advantage. 

It would appear, from a comparison of drawings made at 
different dates, that some nebulae are subject to great changes 
of form. Especially does this hold true of the nebula sur- 
rounding the remarkable variable star »j Argus. In many 
other nebula? changes have been suspected ; but the softness 
and indistinctness of outline which characterize most of these 
objects, and the great difference of their aspect when seen in 
telescopes of very different powers, make it difficult to prove a 
change from mere differences of drawing. One of the strong- 
est cases in favor of change has been made out by Professor 
Holden from a study of drawings and descriptions of what is 
called the " Omega nebula," from a resemblance of one of 



458 



THE STELLAR UNIVERSE. 




Fig. 106. — The Omega nebula; Herschel 2008. Eight ascension, IS hours 13 miuutes; 
declination, 16° 14' S. After Holden and Trouvelot. 

its branches to the Greek letter O. We present a figure of 
this object as it now appears, from a drawing by Professor 
Holden and Mr. Trouvelot, with the great Washington tele- 
scope. It is the branch on the left-hand end of the nebula 
which was formerly supposed to have the form of Q,. 

As illustrative of the fantastic forms which nebulae some- 
times assume, w r e present Herschel's views of two more neb- 
ulae. That shown in Fig. 108 he calls the " looped nebula," 
and describes as one of the most extraordinary objects in the 
heavens. It cannot be seen to advantage except in the south- 
ern hemisphere. 

Distribution of the Nebuhje. — A remarkable feature of the 
distribution of the nebulae is that they are most numerous 
where the stars are least so. While the stars grow thicker as 
we approach the region of the Milky Way, the nebulae dimin- 
ish in number. Sir John Herschel remarks that one-third of 



NEBULAE. 



459 




Fig. 10T. 



-Nebula Uerechel 3722. Right ascension, 17 hours 56 minutes; declination, 24* 
21' S. After Sir John Herschel. 



the nebulous contents of the heavens are congregated in a 
broad, irregular patch occupying about one -eighth the sur- 
face of the celestial sphere, extending from Ursa Major in the 
north to Virgo in the south. If, however, we consider, not the 
true nebulae, but star clusters, we find the same tendency to 
condensation in the Milky Way that we do in the stars. We 
thus have a clearly marked dis- 
tinction between nebulae and 
stars as regards the law of their 
distribution. The law in ques- 
tion can be most easily under- 
stood by the non-mathematical 
reader by supposing the starry 
sphere in such a position that 
the Milky Way coincides witli 
the horizon. Then the stars and 
star clusters will be fewest at the 
zenith, and will increase in number as we approach the horizon. 
Also, in the invisible hemisphere the same law will hold, the 
stars and clusters being fewest under our feet, and will increase 
as we approach the horizon. But the true nebulae will then 




Fig. 10S.— The looped nebula : Herschel 
2941. Right ascension. 5 hours 40 min- 
utes ; declination, 69° 6' S. 



460 THE STELLAR UNIVERSE. 

be fewest in the horizon, and will increase in number as we ap- 
proach the zenith, or as, going below the horizon, we approach 
the nadir. The positions of the nebulae and clusters in Sir John 
Herschel's great catalogue have been studied by Mr. Cleve- 
land Abbe with especial reference to their distance from the 
galactic circle, and the following numbers show part of his re- 
sults. Imagine a belt thirty degrees wide extending around 
the heavens, including the Milky Way, and reaching fifteen 
degrees on each side of the central circle of the Milky Way. 
This belt will include nearly one-fourth the surface of the ce- 
lestial sphere, and if the stars or nebulae were equally distrib- 
uted, nearly one-fourth of them would be found in the belt. 
Instead, however, of one-fourth, we find nine-tenths of the star 
clusters, but only one-tenth of the nebulae. 

The discovery that the nebulae are probably masses of glow- 
ing gas is of capital importance as tending to substantiate the 
view of Sir William Herschel, that these masses are the crude 
material out of which suns and systems are forming. This 
view was necessarily an almost purely speculative one on the 
part of that distinguished astronomer ; but unless we suppose 
that the nebulae are objects of almost miraculous power, there 
must be some truth in it. A nebulous body, in order to shine 
by its own light, as it does, must be hot, and must be losing 
heat through the very radiation by which we see it. As it 
cools, it must contract, and this contraction cannot cease un- 
til it becomes either a solid body or a system of such bodies 
revolving round each other. We shall explain this more fully 
in treating of cosmical physics and the nebular hypothesis. 

§ 7. Proper Motions of the Stars. 

To the unassisted eye, the stars seem to preserve the same 
relative positions in the celestial sphere generation after gen- 
eration. If Job, Hipparchus, or Ptolemy should again look 
upon the heavens, he would, to all appearance, see Aldebaran, 
Orion, and the Pleiades exactly as he saw them thousands of 
years ago, without a single star being moved from its place. 
But the refined methods of modern astronomy, in which the 



PROPER MOTIONS OF THE STARS. 461 

telescope is brought in to measure spaces absolutely invisible 
to the eye, have shown that this seeming unchangeability is 
not real, and that the stars are actually in motion, only the 
rate of change is so slow that the eye would not, in most cases, 
notice it for thousands of years. In ten thousand years quite 
a number of stars, especially the brighter ones, would be seen 
to have moved, while it would take a hundred thousand years 
to introduce a very noticeable change in the aspect of the con- 
stellations. 

As a general rule, the brighter stars have the greatest 
proper motions. But this is a rule to which there are many 
exceptions. The star which, so far as known, has the greatest 
proper motion of all — namely, Groombridge 1830 — is of the 
seventh magnitude only. Next in the order of proper motion 
conies the pair of stars 61 Cygni, each of which is of the sixth 
magnitude. Next are four or live others of the fourth and 
fifth magnitudes. The annual motions of these stars are as 
follows : 



Groombridge 1830 7".0 

61 Cygni 5". 2 

Lalande 21185 4". 7 

e Indi 4".fi 



Lalande 21258 4 .4 

o 2 Eridani 4".l 

p. Cassiopeia 3". 8 

a Ceutauri 3.7 



The first of these stars, though it has the greatest proper 
motion of all, would require 185,000 years to perform the 
circuit of the heavens, while jjl Cassiopeia^ would require near- 
ly 3-10,000 years to perform the same circuit. Slow as these 
motions are, they are very large compared with those of most 
of the stars of corresponding magnitude. As a general rule, 
the stars of the fourth, fifth, and sixth magnitudes move only 
a few seconds in a hundred years, and would therefore re- 
quire many millions of years to perform the circuit of the 
heavens. 

So far as they have yet been observed, and, indeed, so far 
as they can be observed for many centuries to come, these 
motions take place in perfectly straight lines. If each star is 
moving in some orbit, the orbit is so immense that no curva- 
ture can be perceived in the short arc which has been de- 



462 THE STELLAR UNIVERSE. 

scribed since accurate determinations of the positions of the 
stars began to be made. So far as mere observation can in- 
form us, there is no reason to suppose that the stars are sever- 
ally moving in definite orbits of any kind. It is true that 
Madler attempted to show, from an examination of the proper 
motions of the stars, that the whole stellar universe was revolv- 
ing around the star Alcyone, of the Pleiades, as a centre — a 
theory the grandeur of which led to its wide diffusion in popu- 
lar writings. But not the slightest weight has ever been given 
it by astronomers, who have always seen it to be an entirely 
baseless speculation. If the stars were moving in any regular 
circular orbits whatever having a common centre, we could 
trace some regularity among their proper motions. But no 
such regularity can be seen. The stars in all parts of the 
heavens move in all directions, with all sorts of velocities. It 
is true that, by averaging the proper motions, as it were, we 
can trace a certain law in them ; but this law indicates, not a 
particular kind of orbit, but only an apparent proper motion, 
common to all the stars, which is probably due to a real mo- 
tion of our sun and solar system. 

The Solar Motion. — As our sun is merely one of the stars, 
and rather a small star too, it may have a proper motion as 
well as the other stars. Moreover, when we speak of the 
proper motion of a star, we mean, not its absolute motion, but 
only its motion relative to our system. As the sun moves, he 
carries the earth and all the planets along with him ; and if 
we observe a star at perfect rest while we ourselves are thus 
moving, the star will appear to move in the opposite direc- 
tion, as we have already shown in explaining the Copernican 
system. Hence, from an observation of the motion of a sin- 
gle star, it is impossible to decide how much of this apparent 
motion is due to the motion of our system, and how much to 
the real motion of the star. If, however, we should observe a 
great number of stars on all sides of us, and find them all ap- 
parently moving in the same direction, it would be natural to 
conclude that it was really our system which was moving, and 
not the stars. Now, when Herschel averaged the proper mo- 



PROPER MOTIONS OF THE STARS. 



463 



tions of the stars in different regions of the heavens, he found 
that this was actually the case. In general, the stars moved 
from the direction of the constellation Hercules, and towards 
the opposite point of the celestial sphere, near the constella- 
tion Argus. This would show that, relatively to the general 
mass of the stars, our sun was moving in the direction of the 
constellation Hercules. IlersehePs data for this conclusion 
were, necessarily, rather slender. The subject was afterwards 
very carefully investigated by Argelander, and then by a num- 
ber of other astronomers, whose results for the point of the 
heavens towards which the sun is moving are as follows : 





Right Ascension. 


Deelinition. 


Argelander 


257° 49' 
261° 22' 
252 24' 
260 1 
261° 38' 
202° 29' 


28° 50' N. 
37° 36' X. 
14° 26 N. 
34 23' X. 

39 r,i X. 

28° :>8' N. 


(). Strove 


Lundahl 


Madler 


Airy and Dunkin 



It will be seen that while there is a pretty wide range among 
the authorities as to the exact point, and, therefore, some un- 
certainty as to where we should locate it, yet, if we lay the 
different points down on a star-map, we shall find that they 
all fall in the constellation Hercules, which was originally as- 
signed by Herschel as that towards which we were moving. 

As to the amount of the motion, Struve found that if the 
sun were viewed from the distance of an average star of the 
first magnitude placed in a direction from us at right angles 
to that of the solar motion, it would appear to move at the 
rate of 33".9 per century. Dunkin found the same motion to 
be 33".5 or 41".0, according to the use he made of stars hav- 
ing large proper motions. 

Motion of Groups of Stars. — There are in the heavens sev- 
eral cases of widely extended groups of stars, having a com- 
mon proper motion entirely different from that of the stars 
around and among them. Such groups must form connected 
svstems, in the motion of which all the stars are carried alon<r 
together without anv great change in their positions relative 

31 " 






464 THE STELLAR UNIVERSE. 

to each other. The most remarkable case of this kind oc- 
curs in the constellation Taurus. A large majority of the 
brighter stars in the region between Aldebaran and the Plei- 
ades have a common proper motion of about ten seconds per 
century towards the east. How many stars are included in 
this group no one knows, as the motions of the brighter ones 
only have been accurately investigated. Mr. R. A. Proctor 
has shown that five out of the seven stars which form the 
Dipper, or Great Bear, are similarly connected. He proposes 
for this community of proper motions in certain regions the 
name of Star-drift. Besides those we have mentioned, there 
are cases of close groups of stars, like the Pleiades, and of 
pairs of widely separated stars, in which star -drift has been 
noticed. 

Motion in the Line of Sight. — Until quite recently, the only 
way in which the proper motion of a star could be detected 
was by observing its change of direction, or the change of the 
point in which it is seen on the celestial sphere. It is, how- 
ever, impossible in this way to decide whether the star is or is 
not changing its distance from our system. If it be moving 
directly towards us, or directly away from us, we could not 
see any motion at all. The complete motion of the stars can- 
not, therefore, be determined by mere telescopic observations. 
But there is an ingenious method, founded on the undulatory 
theory of light, by which this motion may be detected with 
more or less probability by means of the spectroscope, and 
which was first successfully applied by Mr. Huggins, of Eng- 
land. According to the usual theory of light, the luminosity 
of a heated body is a result of the vibrations communicated 
by it to the ethereal medium which fills all space ; and if the 
body be gaseous, it is supposed that a molecule of the gas vi- 
brates at a certain definite rate, and thus communicates only 
certain definite vibrations to the ether. The rate of vibration 
is determined by the position of the bright line in the spec- 
trum of the gas. Now, if the vibrating body be moving 
through the ether, the light-waves which it throws behind it 
will be longer, and those which it throws in front of it will be 



PROPER MOTIONS OF THE STARS. 465 

shorter, than if the body were at rest. The result will be, that 
in the former case the spectral lines will be less refrangible, 
or nearer the red end of the Bpectrum, and in the latter case 
nearer the blue end. If the line is not a bright one which the 
gas emits, but the corresponding dark one which it has ab- 
sorbed from the light of a star passing through it, the result 
will be the same. If such a known line is found slightly 
nearer the blue end of the spectrum than it should be, it is 
concluded that the star from which it emanates is approach- 
ing us, while in the contrary case it is receding from us. 

The question may be asked, How can we identify a line as 
proceeding from a gas, unless it is exactly in the position of 
the line due to that gas ? How do we know but that it may 
be due to some other gas which emits light of slightly differ- 
ent refrangibility ? The reply to this must be, that absolute 
certainty on this point is not attainable ; but that, from the 
examination of a number of stars, the probabilities seem large- 
ly in favor of the opinion that the displaced lines are really 
due to the gases near whose lines they fall. If the lines were 
always displaced in one direction, whatever star was exam- 
ined, the conclusion in question could not be drawn, because 
it might be that this line was due to some other unknown sub- 

CD 

stance. But as a matter of fact, when different stars are ex- 
amined, it is found that the lines in question are sometimes 
on one side of their normal position and sometimes on the 
other. This makes it probable that they really all belong to 
one substance, but are displaced by some cause, and the motion 
of the star is a cause the existence of which is certain, and the 
sufficiency of which is probable. 

Mr. Huggins's system of measurement has been introduced 
by Professor Airy into the Eoyal Observatory, Greenwich, 
where very careful measures have been made during the past 
two years by Mr. Christie and Mr. Maunder. To show how 
w T ell the fact of the motion is made out, we give in the tables 
on the following page the results obtained by Mr. Huggins 
and by the Greenwich observers for those stars in which the 
motion is the largest : 



466 



THE STELLAR UNIVERSE. 



STARS RECEDING FROM US. 





By Mr. Huggins. 


By Greenwich. 


Sirius 


20 miles per sec. 

22 " 

15 " 

25 " 

15 " " 


25 miles per sec. 

76 " " 

receding. 

25 miles per sec. 

30 " " 


a ( )rion i s 




a Geminorum 


a Leon is 





STARS APPROACHING US. 



Arc turns 
a Lyras .. 



a Cygni 

j3 Geminorum... 
a Ursae Majoris. 



By Mr. Huggins. 



55 miles per sec. 

50 " 

39 " " 

49 " 

46 " 



By Greenwich. 



41 miles per sec. 
36 " 
41 " 

approaching, 
approaching. 



There are several collateral circumstances which tend to 
confirm these results. One is that the general amount of mo- 
tion indicated is, in a rough way, about what we should expect 
the stars to have, from their observed proper motions, com- 
bined with their probable parallaxes. Another is that those 
stars in the neighborhood of Hercules are mostly found to be 
approaching the earth, and those which lie in the opposite di- 
rection to be receding from it, which is exactly the effect which 
would result from the solar motion just described. Again, the 
five stars in the Dipper which we have described as having a 
common proper motion are also found to have a common mo- 
tion in the line of sight. The results of this wonderful and 
refined method of determining stellar motion, therefore, seem 
worthy of being received with some confidence so far as the 
general direction of the motion is concerned. But the dis- 
placement of the spectral lines is so slight, and its measure- 
ment a matter of such difficulty and delicacy, that we are far 
from being sure of the exact numbers of miles per second 
given by the observers. The discordances between the results 
of Greenwich and those of Mr. Huggins show that numerical 
certainty is not yet attained. 

A necessary result of these motions will be that those stars 
which are receding from us will, in the course of ages, appear 
less brilliant, owing to their greater distance, while those which 






V HOVER MOTIONS OF THE STARS. 467 

are approaching us will, as they come nearer, appear brighter, 
always supposing that their intrinsic brightness does not vary. 
But so immense is the distance of the stars, that many thou- 
sands of years will be required to produce any appreciable 
change in their brightness from this cause. For instance, 
from the best determinations which have been made, the dis- 
tance of Si rill 8 from our system is more than a million radii 
of the earth's orbit. With a velocity of twenty miles per sec- 
ond, it would require more than one hundred and fifty thou- 
sand years to pass over this distance. 

It will, of course, be understood that the velocities found by 
the spectroscopic method are not the total velocities with 
which the stars are moving, but only the rate at which they 
are approaching to or receding from the earth, or, to speak 
mathematically, the component of the velocity in the direc- 
tion of the line of sight. To find the total velocity, this com- 
ponent must be combined with the telescopic velocity found 
from the observed proper motion of the star, which is the ve- 
locity at right angles to the line of sight. None of the stars 
are moving exactly towards our system, and it is not likely 
that any will ever pass very near it. In the preceding list, 
the star a Cygni is the one which is coming most directly 
towards us. Its telescopic proper motion is so slight that, 
though we suppose its distance to be two million radii of the 
earth's orbit, yet its velocity at right angles to the line of sight 
will hardly amount to one-third of a mile per second. If the 
spectroscopic determination is correct, then, after an interval 
which will probably fall between one hundred thousand and 
three hundred thousand years, a Cygni will pass by our sys- 
tem at something like a hundredth of its present distance, 
and will, for several thousand years, be many times nearer and 
brighter than any star is now. 



4(38 THE STELLAR UNIVERSE. 



CHAPTER II. 

THE STRUCTURE OF THE UNIVERSE. 

Haying in the preceding chapter described those features 
of the universe which the telescope exhibits to us, we have 
now, in pursuance of our plan, to inquire what light telescopic 
discoveries can throw upon the structure of the universe as a 
whole. Here we necessarily tread upon ground less sure than 
that which has hitherto supported us, because we are on the 
very boundaries of human knowledge. Many of our conclu- 
sions must be more or less hypothetical, and liable to be modi- 
fied or disproved by subsequent discoveries. We shall en- 
deavor to avoid all mere guesses, and to state no conclusion 
which has not some apparent foundation in observation or 
analogy. The human mind cannot be kept from speculating 
upon and wondering about the order of creation in its widest 
extent, and science will be doing it a service in throwing ev- 
ery possible light on its path, and preventing it from reaching 
any conclusion inconsistent with observed facts. 

The first question which we reach in regular order is, How 
are the forty or fifty millions of stars visible in the most pow- 
erful telescopes arranged in space? We know, from direct 
observation, how they are arranged with respect to direction 
from our system ; and we have seen that the vast majority of 
small stars visible in great telescopes are found in a belt span- 
ning the heavens, and known as the Milky Way. But this 
gives us no complete information respecting their absolute po- 
sition : to determine this, we must know the distance as well 
as the direction of each star. But beyond the score or so of 
stars which have a measurable parallax, there is no known 
way of measuring the stellar distances ; so that all we can do 



VIEWS OF MODERN ASTRONOMERS. 469 

is to make more or less probable conjectures, founded on the 
apparent magnitude of the individual stars and the probable 
laws of their arrangement. If the stars were all of the same 
intrinsic brightness, we could make a very good estimate of 
their distance from their apparent magnitude ; but we know 
that such is not the case. Still, in all reasonable probability, 
the diversity of absolute magnitude is far less than that of the 
apparent magnitude; so that a judgment founded on the lat- 
ter is much better than none at all. It was on such consider- 
ations as these that the conjectures of the first observers with 
the telescope were founded. 

§ 1. Views of Astronomers before Herschel. 

Before the invention of the telescope, any well-founded 
opinion respecting the structure of the starry system was out 
of the question. We have seen how strong a hold the idea of 
a spherical universe had on the minds of men, so that even 
Copernicus was fully possessed with it, and probably believed 
the sun to be, in some way, the centre of this sphere. Before 
any step could be taken towards forming a true conception of 
the universe, this idea had to be banished from the mind, and 
the sun had to be recognized as simply one of innumerable 
stars which made up the universe. The possibility that such 
might have been the case seems to have first suggested itself 
to Kepler, though he was deterred from completely accepting 
the idea by an incorrect estimate of the relative brilliancy of 
the stars. lie reasoned that if the sun were one of a vast 
number of fixed stars of equal brilliancy scattered uniformly 
throughout space, there could not be more than twelve which 
were at the shortest distance from us. We should then have 
another set at double the distance, another at triple the dis- 
tance, and so on ; and since the more distant they are, the 
fainter they would appear, we should speedily reach a limit 
beyond which no stars could be seen. In fact, however, we 
often see numerous stars of the same magnitude crowded 
closeh 7 together, as in the belt of Orion, while the total num- 
ber of visible stars is reckoned by thousands. He therefore 



470 THE STELLAR UNIVERSE. 

concludes that the distances of the individual stars from each 
other are much less than their distances from our sun, the lat- 
ter heing situated near the centre of a comparatively vacant 
region. 

Had Kepler known that it would require the light of a hun- 
dred stars of the sixth magnitude to make that of one of the 
first magnitude, he would not have reached this conclusion. 
A simple calculation would have shown him that, with twelve 
stars at distance unity, there would have been four times that 
number at the double distance, nine times at the treble dis- 
tance, and so on, until, within the tenth sphere, there would 
have been more than four thousand stars. The twelve hun- 
dred stars on the surface of the tenth sphere would have 
been, by calculation, of the sixth magnitude, a number near 
enough to that given by actual count to show him that the 
hypothesis of a uniform distribution was quite accordant with 
observations. It is true that, where many bright stars were 
found crowded together, as in Orion, their distance from each 
other is probably less than that from our sun. But this ag- 
glomeration, being quite exceptional, would not indicate a gen- 
eral crowding together of all the stars, as Kepler seemed to 
suppose. In justice to Kepler it must be said that he put 
forth this view, not as a well-founded theory, but only as a 
surmise, concerning a question in which certainty was not 
attainable. 

Ideas of Kant. — Those who know of Kant only as a specula- 
tive philosopher may be surprised to learn that, although he 
was not a working astronomer, he was the author of a theory 
of the stellar system which, with some modifications, has been 
very generally held until the present time. Seeing the Gal- 
axy encircle the heavens, and knowing it to be produced by 
the light of innumerable stars too distant to be individually 
visible, he concluded that the stellar system extended much 
farther in the direction of the Galaxy than it did elsewhere. 
In other words, he conceived the stars to be arranged in a 
comparatively thin, flat layer, or stratum, our sun being some- 
where near the centre. When we look edgewise along this 



VIEWS OF MODERN ASTRONOMERS. 471 

stratum, we see an immense number of stars, but in the per- 
pendicular direction comparatively few are visible.* 

This thin stratum suggested to Kant the idea of a certain 
resemblance to the solar system. Owing to the small inclina- 
tions of the planetary orbits, the bodies which compose this 
system are spread out in a thin layer, as it were ; and we have 
only to add a great multitude of planets moving around the 
sun in orbits of varied inclinations to have a representation in 
miniature of the stellar system as Kant imagined it to exist. 
Had the zone of small planets between Mars and Jupiter then 
been known, it would have afforded a striking confirmation of 
Kant's view by showing a yet greater resemblance of the plan- 
etary system to his supposed stellar system. Were the num- 
ber of these small planets sufficiently increased, we should see 
them as a sort of Galaxy around the zodiac, a second Milky 
Way, belonging to our system, and resolvable with the tele- 
scope into small planets, just as the Galaxy is resolved into 
small stars. The conclusion that two systems which were so 
similar in appearance were really alike in structure would 
have seemed very well founded in analogy. 

As the planets are kept at their proper distances, and pre- 
vented from falling into each other or into the sun by the 
centrifugal force generated by their revolutions in their or- 
bits, so Kant supposed the stars to be kept apart by a revolu- 
tion around some common centre. The proper motions of 
the stars were then almost unknown, and the objection was 
anticipated that the stars were found to occupy the same po- 
sition in the heavens from generation to generation, and there- 
fore could not be in motion around a centre. To this Kant's 
reply was that the time of revolution w r as so long, and the 
motion so slow, that it was not perceptible with the imper- 
fect means of observation then available. Future genera- 
tions would, he doubted not, by comparing their observations 



* The original idea of this theory is attributed by Kant to Wright, of Durham. 
England, a writer whose works are entirely unknown in this country, and whose 
authorship of the theory has been very generally forgotten. 



472 THE STELLAR UNIVERSE. 

with those of their predecessors, find that there actually was a 
motion among the stars. 

This conjecture of Kant, that the stars would be found to 
have a proper motion, has, as we have seen, been amply con- 
firmed ; but the motion is not of the kind which his theory 
would require. On this theory, all the stars ought to move in 
directions nearly parallel to that of the Milky Way, just as in 
the planetary system we find them all moving in directions 
nearly parallel to the ecliptic. But the proper motions actually 
observed have no common direction, and follow no law what- 
ever, except that, on the average, there is a preponderance of 
motions from the constellation Hercules, which is attributed 
to an actual motion of our sun in that direction. Making al- 
lowance for this preponderance, we find the stars to be appar- 
ently moving at random in every direction ; and therefore 
they cannot be moving in any regularly arranged orbits, as 
Kant supposed. A defender of Kant's system might indeed 
maintain that, as it is only in a few of the stars nearest us 
that any proper motion has been detected, the great cloud of 
stars which make up the Milky Way might really be moving 
along in regular order, a view the possibility of which we shall 
be better prepared to consider hereafter. 

The Kantian theory supposes the system which we have 
just been describing to be formed of the immense stratum of 
stars which make up the Galaxy and stud our heavens, and 
to include all the stars separately visible with our telescopes. 
But he did not suppose this system, immense though it is, to 
constitute the whole material universe. In the nebulae he 
saw other similar systems at distances so immense that the 
combined light of their millions of suns only appeared as a 
faint cloud in the most powerful telescopes. This idea that 
the nebulae were other galaxies was more or less in Vogue 
among popular writers until a quite recent period, when it 
was refuted by the spectroscope, which shows that these ob- 
jects are for the most part masses of glowing gas. It has, 
however, not received support among astronomers since the 
time of Sir William Herschel. 



RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 473 

System of Lambert. — A few years after the appearance of 
Kant's work, a similar but more elaborate system was sketched 
out by Lambert. lie supposed the universe to be arranged in 
systems of different orders. The smallest systems which we 
know are those made up of a planet, with its satellites circu- 
lating around it as a centre. The next system in order of 
magnitude is a solar system, in which a number of smaller 
systems are each carried round the sun. Each individual star 
which we see is a sun, and has its retinue of planets revolving 
around it, so that there are as many solar systems as stars. 
These systems are not, however, scattered at random, but are 
divided up into greater systems which appear in our telescopes 
as clusters of stars. An immense number of these clusters 
make up our Galaxy, and form the visible universe as seen in 
our telescopes. There may be yet greater systems, each made 
up of galaxies, and so on indefinitely, only their distance is so 
immense as to elude our observation. 

Each of the smaller systems visible to us has its central body, 
the mass of which is much greater than that of those which 
revolve around it. This feature Lambert supposed to extend 
to other systems. As the planets are larger than their satel- 
lites, and the sun larger than its planets, so he supposed each 
stellar cluster to have a great central body around which each 
solar system revolved. As these central bodies are invisible to 
us, he supposed them to be opaque and dark. All the systems, 
from the smallest to the greatest, were supposed to be bound 
together bv the one universal law of gravitation. 

As not the slightest evidence favoring the existence of these 
opaque centres has ever been found, we are bound to say that 
this sublime idea of Lambert's has no scientific foundation. 
Astronomers have handed it over without reservation to the 
lecturers and essayists. 

§ 2. Researches of Hersehel and his Successors. 

Herschel was the first who investigated the structure of 
the stellar system by a long-continued series of observations, 
executed with a definite end in view. His plan was that of 



474 THE STELLAR UNIVERSE. 

" star - ganging," which meant, in the first place, the simple 
enumeration of all the stars visible with a powerful tele- 
scope in a given portion of the heavens. He employed a 
telescope of twenty inches aperture, magnifying one hundred 
and sixty times, the field of view being a quarter of a degree 
in diameter. This diameter was about half that of the full 
moon, so that each count or gauge included all the stars visi- 
ble in a space having one-fourth the apparent surface of the 
lunar disk. From the number of stars in any one field of 
view, he concluded to w T hat relative distance his sight ex- 
tended, supposing a uniform distribution of the stars through- 
out all the space included in the cone of sight of the telescope. 
When an observer looks into a telescope pointed at the heav- 
ens, his field of vision includes a space which constantly 
widens out on all sides as the distance becomes greater ; and 
the reader acquainted with geometry will see that this space 
forms a cone having its point in the focus of the telescope, and 
its circular base at the extreme distance to which the telescope 
reaches. The solid contents of this cone will be proportional 
to the cube of the distance to which it extends ; for instance, 
if the telescope penetrates twice as far, the cone of sight will 
be not only twice as long, but the base will be twice as wide 
in each direction, so that the cone will have altogether eight 
times the contents, and will, on Hersehel's hypothesis, contain 
eight times as many stars. So, when Herschel found the stars 
eight times as numerous in one region as in another, he con- 
cluded that the stellar system extended twice as far in the 
direction of the first region. 

To count all the stars visible with his telescope, Herschel 
found to be out of the question. He would have had to point 
his instrument several hundred thousand times, and count all 
the visible stars at each pointing. He therefore extended his 
survey only over a wide belt extending more than half-way 
round the celestial sphere, and cutting the Galaxy at right 
angles. In this belt he counted the stars in 3400 telescopic 
fields. Comparing the average number of stars in different 
regions with the position of the region relative to the Galaxy, 



RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 475 

he found that the stars were thinnest at the point most distant 
from the Galaxy, and that they constantly increased in num- 
ber as the Galaxy was approached. The following table will 
give an idea of the rate of increase. It shows the average 
number of stars in the field of view of the telescope for each 
of six zones of distance from the Galaxy. 

First zone 90° to 75° from Galaxy 4 stars per field. 

Second zone 75° " GO " " "> " 

Third zone 60° " 45° " " H " 

Fourth zone 45° " 30° " " 14 " 

Fifth zone 30° " 15° " " 24 " 

Sixth zone 15° " 0° " " 53 " 

A similar enumeration was made by Sir John Ilerschel for the 
corresponding region on the other, or southern, side of the Gal- 
axy. He used the same telescope, and the same magnifying 
power. His results were : 



First zone G stars per field. 

Second zone 7- " " 

Third zone 9 " 



Fourth zone 13 stars per field. 

Fifth zone 2G " " 

Sixth zone 59 " " 



The reader will, perhaps, more readily grasp the significa- 
tion of these numbers by the mode of representation which 
was suggested in describing the distribution of the nebula*. 
Let him imagine himself standing under a clear sky at the 
time when the Milky Way encircles the horizon. Then, the 
first zone, as we have defined it, will be around the zenith, ex- 
tending one -sixth of the way to the horizon on every side; 
the second zone will be next below and around this circular 
space, extending one-third of the way to the horizon ; and so 
each one will follow in regular order until we reach the sixth, 
or galactic, zone, which will encircle the horizon to a height 
of 15° on every side. The numbers we have given show that 
in the position of the observer which we have supposed the 
stars would be thinnest around the zenith, and would con- 
stantly increase in number as we approached the horizon. 
The observer being supposed still to occupy the same posi- 
tion, the second table shows the distribution of the stars in the 



476 THE STELLAR UNLVEBSE. 

opposite or invisible hemisphere, which he would see if the 
earth were removed. In this hemisphere the first, or thinnest, 
zone would be directly opposite the thinnest zone in the ob- 
server's zenith ; that is, it would be directly under his feet. 
The successive zones would then be nearer the horizon, the 
sixth or last encircling it, and extending 15° below it on every 
side. 

The numbers we have given are only averages, and do not 
give an adequate idea of the actual inequalities of distribu- 
tion in special regions of the heavens. Sometimes there was 
not a solitary star in the field of the telescope, while at oth- 
ers there were many hundreds. In the circle of the Galaxy 
itself, the stars are more than twice as thick as in the average 
of the first zone, which includes not only this circle, but a 
space of 15° on each side of it. 

Adopting the hypothesis of a uniform distribution of the 
stars, Herschel concluded from his first researches that the 
stellar system was of the general form supposed by Kant, ex- 
tending out on all sides five times as far in the direction of 
the Galaxy as in the direction perpendicular to it. The most 
important modification he made was to suppose an immense 
cleft extending edgewise into the system from its circumfer- 
ence about half-way to the centre. This cleft corresponded to 
the division in the Milky Way which commences in the sum- 
mer constellation Cygnus in the north, and passes through 
Aquila, the Serpent, and Scorpius far into the southern hemi- 
sphere. Estimating the distance by the arrangement and ap- 
parent magnitude of the stars, he w T as led to estimate the mean 
thickness of the stellar stratum from top to bottom as 155 
units, and the diameter as 850 units, the unit being the aver- 
age distance of a star of the first magnitude. Supposing this 
distance to be that which light would travel over in 16 years 
— a supposition which is founded on the received estimate of 
the mean parallax corresponding to stars of that magnitude — 
then it would take light nearly 14,000 years to travel across 
the system from one border to the other, and 7000 years to 
reach us from the extreme boundary. 



RESEARCHES OF HERSCHEL AND HIS SUCCE8S0R8. 477 



The foregoing deduction of 
Herschel was founded on the 
hypothesis that the stars were 
equally dense in every part of 
the stellar system, so that the 
number of stars in any direc- 
tion furnished an index to the 
extent of the stars in that di- 
rection. Further study show- 
ed Herschel that this assump- 
tion might be so far from cor- 
rect that his conclusions would 
have to be essentially modi- 
fied. Binary and other double 
stars and star clusters evident- 
ly offered cases in which sev- 
eral stars were in much closer 
association than were the stars 
in general. To show exactly 
on what considerations this 
change of view is founded, we 
remark that if the increase of 
density in the direction of the 
Milky Way were quite regu- 
lar, so that there were no cases 
of great difference in the thick- 
ness of the stars in two adjoin- 
ing regions, then the original 
view would have been sound 
so far as it went. But such ir- 
regularities are very frequent, 
and it would lead to an obvi- 
ous absurdity to explain them 
on Herschel's first hypothesis ; 
for instance, when the tele- 
scope was directed towards 
the Pleiades there would be FlGi 




. — Herschel's view of the form of the 
universe. 



4:78 TEE STELLAR UNIVERSE. 

found, probably, six or eight times as many stars as in the ad- 
joining fields. But supposing the real thickness of the stars 
the same, the result would be that in this particular direction 
the stars extended out twice as far as they did in the neigh- 
boring parts of the sky ; that is, we should have a long, nar- 
row spike of stars pointing directly from us. As there are 
many such clusters in various parts of the sky, we should have 
to suppose a great number of such spikes. In other regions, 
especially around the Milky Way, there are spaces nearly void 
of stars. To account for these we should have to suppose 
long narrow chasms reaching through towards our sun. Thus 
the stellar system would present the form of an exaggerated 
star-fish with numerous deep openings, a form the existence 
of which is beyond all probability, especially if we reflect 
that all the openings and all the arms have to proceed from 
the direction of our sun. 

The only rational explanation of a group of stars showing 
itself in a telescope, with a comparatively void space surround- 
ing it, is that we have here a real star cluster, or a region in 
which the stars are thicker than elsewhere. Now, one can see 
with the naked eye that the Milky Way is not a continuous 
uniform belt, but is, through much of. its course, partly made 
up of a great number of irregular cloud-like masses with com- 
paratively dark spaces between them. The conclusion is un- 
avoidable that we have here real aggregations of stars, and 
not merely a region in which the bounds of the stellar-sys- 
tem are more widely extended. Whether Herschel clearly saw 
this m&y be seriously questioned ; but however it may have 
been, he adopted another method of estimating the relative 
distances of the stars visible in his gauges. 

This method consisted in judging of the distances to which 
his telescope penetrated, not by the number of stars it brought 
into view, but by their brightness. If all the stars were of the 
same intrinsic brightness, so that the differences of their ap- 
parent magnitude arose only from their various distances from 
us, then this method would enable us to fix the distance of 
each separate star. But as we know that the stars are by no 






RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 470 



means equal in intrinsic brightness, the method cannot be 
safely applied to any individual star, a fact which Herschel 
himself clearly saw. It does not follow, however, that we 
cannot thus form an idea of the relative distances of whole 
classes or groups of stars. Although it is quite possible that 
an individual star of the fifth magnitude may be nearer to us 
than another of the fourth, yet we cannot doubt that the av- 
erage distance of all the fifth-magnitude stars is greater than 
the average of those of the fourth magnitude, and greater, 
too, in a proportion admitting of a tolerably accurate numeri- 
cal estimate. Such an estimate Herschel attempted to make, 
proceeding on the following plan : 

Suppose a sphere to be drawn around our sun as a centre 
of such size that it shall be 
equal to the average space 
occupied by a single one of 
the stars visible to the naked 
eye; that is, if we suppose 
that portion of the space of 
the stellar system occupied 
by the six thousand bright- 
er stars to be divided into 
six thousand parts, then the 
sphere will be equal to one 
of these parts. The radius 
of this sphere will probably 
not differ much from the dis- 
tance of the nearest fixed star, 
a distance we shall take for 
unity. Then, suppose a series 
of larger spheres, all drawn 
around our sun as a centre, 
and having the radii 3, 5, 7, 
9, etc. The contents of the 
spheres being as the cubes 
of their diameters, the first 
sphere will have 3 x 3 x 3=27 




-Illustrating Herschel's orders of dis- 
tance of the stars. • 



32 



4S0 



THE STELLAR UNIVERSE. 



times the bulk of the unit sphere, and will therefore be large 
enough to contain 27 stars; the second will have 125 times 
the bulk, and will therefore contain 125 stars, and so with 
the successive spheres. Fig. 110 shows a section of portions 
of these spheres up to that with radius 11. Above the centre 
are given the various orders of stars which are situated be- 
tween the several spheres, while in the corresponding spaces 
below the centre are given the number of stars which the re- 
gion is large enough to contain ; for instance, the sphere of 
radius 7 has room for 343 stars, but of this space 125 parts 
belong to the spheres inside of it : there is, therefore, room for 
218 stars between the spheres of radii 5 and 7. 

Herschel designates the several distances of these layers of 
stars as orders ; the stars between spheres 1 and 3 are of the 
first order of distance, those between 3 and 5 of the second 
order, and so on. Comparing the room for stars between the 
several spheres with the number of stars of the several magni- 
tudes, he found the result to be as follows : 



Order of 
Distance. 


Number of 




Number of 


Stars there 


Magnitude. 


Stars of that 




is room for. 




magnitude. 


i 


26 


1 


17 


2 


98 


2 


57 


3 


218 


3 


206 


4 


386 


4 


454 


5 


602 


5 


1161 


6 


866 


6 


6103 


7 


1178 


7 


6146 


8 


1538 







There is evidently no correspondence between the calculat- 
ed orders of distance and the magnitudes as estimated on the 
usual scale. But Herschel found that this was because the 
magnitudes as usually estimated corresponded to an entirely 
different scale of distance from that which he adopted. In 
his scale the several distances increased in arithmetical pro- 
gression ; while in the order of magnitudes the increase is 
in geometrical progression. In consequence, the stars of the 
sixth magnitude correspond to the eighth, ninth, or tenth order 
of distances ; that is, we should have to remove a star of the 



itESEAECHES OF HERSCHEL AND HIS SUCCESSORS. 4S1 

first magnitude to eight, nine, or ten times its actual distance 
to make it shine as a star of the sixth magnitude. 

Attempting on this system to measure the extent of the 
Milky Way, Herschel concluded that it was unfathomable 
with his twenty -foot telescope, which, he calculated, would 
penetrate to the 900th order of distances, that is, to stars 
which were 900 times as far as the average of those of the 
first magnitude. He does not seem to have made any very 
extended examination with his forty-foot telescope, but con- 
cluded that it would leave him in the same uncertainty in 
respect to the extent of the Milky Way as the twenty-foot one 
did. This unrivalled man, to whom it was given to penetrate 
farther into creation than man had ever done before him, 
seems to have rested from his labors without leaving any more 
definite theory of the boundaries of the stellar system than 
that they extended, at least in the direction of the Milky Way, 
beyond the utmost limit to which his telescope could penetrate. 
If we estimate the time it would require light to come from 
the utmost limit to which he believed his vision to extend, 
Ave shall find it to be about fourteen thousand years, or more 
than double that deduced from his former gauges. We can 
say with confidence that the time required for light to reach 
us from the most distant visible stars is measured by thou- 
sands of years. But it must be admitted that IlersehePs esti- 
mate of the extent of the Milky Way may be far too great, be- 
cause it rests on the assumption that all stars are of the same 
absolute brightness. If the smallest stars visible in his tele- 
scope were, on the average, of the same intrinsic brilliancy as 
the brighter ones, the conclusion would be well founded. But 
if we suppose a boundary, it is impossible to decide from Her- 
schel's data whether the minuteness of those stars arises from 
their great distance or from their small magnitude. Notwith- 
standing this uncertainty, it has been maintained by some, not- 
ably by Mr. Proctor, that the views of Herschel respecting the 
constitution of the Milky Way, or stellar system, were radical- 
ly changed by this second method of star-gauging. I see no 
evidence of any radical change. Although Herschel does not 



±82 THE STELLAR UNIVERSE. 

express himself very definitely on the subject, yet, in his last 
paper on the distribution of the stars {Philosophical Trans- 
actions for 1817), there are several remarks which seem to im- 
ply that he still supposed the stellar system to have the gen- 
eral form shown in Fig. 109, and that, in accordance with that 
view, he supposed the clustering of stars to indicate protuber- 
ant parts of the Milky Way. He did, indeed, apply a differ- 
ent method of research, but the results to which the new meth- 
ods led were, in their main features, the same as those of the 
old method. 

Since the time of Herschel, one of the most eminent of the 
astronomers who have investigated this subject is Struve the 
elder, formerly director of the Pulkowa Observatory. His re- 
searches were founded mainly on the numbers of stars of the 
several magnitudes found by Bessel in a zone thirty degrees 
wide extending all round the heavens, fifteen degrees on each 
side of the equator. With these he combined the gauges of 
Sir William Herschel. The hypothesis on which he based his 
theory was similar to that employed by Herschel in his later 
researches, in so far that he supposed the magnitude of the 
stars to furnish, on the average, a measure of their relative 
distances. Supposing, after Herschel, a number of concentric 
spheres to be drawn around the sun as a centre, the successive 
spaces between which corresponded to stars of the several 
magnitudes, he found that the farther out he went, the more 
the stars were condensed in and near the Milky Way. This 
conclusion may be drawn at once from the fact we have al- 
ready mentioned, that the smaller the stars, the more they are 
condensed in the region of the Galaxy. Struve found that if 
we take only the stars plainly visible to the naked eye — that 
is, those down to the fifth magnitude — they are no thicker in 
the Milky Way than in other parts of the heavens. But those 
of the sixth magnitude are a little thicker in that region, those 
of the seventh yet thicker, and so on, the inequality of distri- 
bution becoming constantly greater as the telescopic power is 
increased. 

From all this, Struve concluded that the stellar system might 



RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 483 

be considered as composed of layers of stars of various densi- 
ties, all parallel to the plane of the Milky Way. The stars are 
thickest in and near the central layer, which he conceives to 
be spread out as a wide, thin sheet of stars. Our sun is situ- 
ated near the middle of this layer. As we pass out of this 
layer, on either side we find the stars constantly growing thin- 
ner and thinner, but we do not reach any distinct boundary. 
As, if we could rise in the atmosphere, we should find the air 
constantly growing thinner, but at so gradual a rate of prog- 
ress that we could hardly say where it terminated ; so. on 
Struve's view, would it be with the stellar system, if we could 
mount up in a direction perpendicular to the Milky Way. 
Struve gives the following table of the thickness of the stars 
on each side of the principal plane, the unit of distance being 
that of the extreme distance to which Ilerschel's telescope 
could penetrate : 









Mean 1 1 


Die 


timet: from Principal Plane. 


Density. 


t>tt\v.-. 
boritm E 


In the 


principal plane 


1.0000 


1.000 


<>.(>:> f 


•urn principal piano. 


0.48568 


1.272 


0.10 


(i (i 


0.33288 


1.458 


0.20 


" " 


0.23895 • 


1.611 


0.30 


" '• 


0.17980 


1.772 


0.40 


11 " 


0.13021 


1.973 


o.r>o 


(< (< 


0.08646 


2.261 


0.00 


(< it 


0.05510 


2.628 


0. 70 


(( (C 


0.03079 


3.190 


0.80 


( . (C 


0.01414 


4.131 


0.866 


l< ct 


0.00532 


5.729 



This condensation of the stars near the central plane, and 
the gradual thinning-out on each side of it, are only designed 
to be the expression of the general or average distribution 
of those bodies. The probability is that even in the central 
plane the stars are many times as thick in some regions as in 
others, and that as we leave the plane, the thinning-out would 
be found to proceed at very different rates in different re- 
gions. That there may be a gradual thinning -out cannot be 
denied ; but Struve's attempt to form a table of it is open to 
the serious objection that, like Herschel, he supposed the dif- 



484 THE STELLAR UNIVERSE. 

ferences between the magnitudes of the stars to arise entirely 
from their different distances from us. Although where the 
scattering of the stars is nearly uniform this supposition may 
not lead us into serious error, the case will be entirely differ- 
ent where we have to deal with irregular masses of stars, and 
especially where our telescopes penetrate to the boundary of 
the stellar system. In the- latter case we cannot possibly dis- 
tinguish between small stars lying within the boundary and 
larger ones scattered outside of it, and Strnve's gradual thin- 
ning-out of the stars may be entirely accounted for by great 
diversities in the absolute brightness of the stars. 

Among recent researches on this subject, those of Mr. R. 
A. Proctor are entitled to consideration, from being founded 
on facts which were not fully known or understood by the 
investigators whom we have mentioned. The strongest point 
which he makes is that all views of the arrangement of the 
stellar system founded upon the theory that the stars are 
either of similar intrinsic brightness, or approach an equality 
of distribution in different regions, are entirely illusory. He 
cites the phenomena of star-drift, described in the last chap- 
ter, as proving that stars which had been supposed widely sep- 
arated are really agglomerated into systems ; and claims that 
the Milky Way may be a collection of such systems, having 
nothing like the extent assigne'd it by Herschel. 

How far the considerations brought forward by Mr. Proc- 
tor should make us modify the views of the subject hitherto 
held, cannot be determined without further observations on the 
clustering of stars of different magnitudes. We may, howev- 
er, safely concede that there is a greater tendency among the 
stars to be collected into groups than was formerly supposed. 
A curious result of Mr. J. M. Wilson, of Rugby, England, re- 
specting the orbits of some binary stars, throws light on this 
tendency. It was found by Struve that although the great 
common proper motion of the pair of stars 61 Cygni, cele- 
brated for the determinations of their parallax, was such as to 
leave no reasonable doubt that they were physically connect- 
ed, yet not the slightest deviation in their courses, arising 



RESEARCHES OF HERSCHEL AND HIS SUCCESSORS. 485 

from their mutual attraction, could be detected. Mr. Wilson 
has recently confirmed this result by an examination of the 
whole series of measures on this pair from 1753 to 1874, 
which do not show the slightest deviation, but seem to indi- 
cate that each star of the pair is going on its course indepen- 
dently of the other. But, as just stated, they move too nearly 
together to permit of the belief that they are really indepen- 
dent. The only conclusion open to us is that each of them de- 
scribes an immense orbit around their common centre of gray- 
ity, an orbit which may be several degrees in apparent diam- 
eter, and in which the time of revolution is counted by thou- 
sands of years. Two thousand years hence they will be so 
far apart that no connection between them would be sus- 
pected. 

It is a question whether we have not another instance of 
the same kind in the double star Castor, or a Geminorum. 
Mr. Wilson finds the orbit of this binary to be apparently 
hyperbolic, a state of things which would indicate that the 
two stars had no physical connection whatever, but that, in 
pursuing their courses through space, they chanced to come 
so close together that they were brought for a while within 
each other's sphere of attraction. If this be the case, they 
will gradually separate forever, like two ships meeting on the 
ocean and parting again. We remark that the course of each 
star will then be very different from what it would have 
been if they had not met. We cannot, however, accept the 
hyperbolic orbit of Mr. Wilson as an established fact, because 
the case is one in which it is very difficult to distinguish be- 
tween a large and elongated elliptic orbit and a hyperbolic 
orbit. The common proper motion of the two objects is such 
as to lead to the belief that they constitute a pair, the compo- 
nents of which separate to a great distance. 

Now, these discoveries of pairs of stars moving around a 
common centre of gravity, in orbits of immense extent, sug- 
gest the probability that there exist in the heavens great num- 
bers of pairs, clusters, and systems of this sort, the members 
of which are so widely separated that they have never been 



4S6 



THE STELLAR UNIVERSE. 



suspected to belong together, and the widely scattered groups 
having a common proper motion may very well be systems of 
this kind. 

§ 3. Probable Arrangement of the Visible Universe. 

The preceding description of the views held by several gen- 
erations of profound thinkers and observers respecting the 
arrangement of the visible universe furnishes an example of 
what we may call the evolution of scientific knowledge. Of 
no one of the great men whom we have mentioned can it be 
said that his views were absolutely and unqualifiedly errone- 
ous, and of none can it be said that he reached the entire 
truth. Their attempts to solve the mystery which they saw 
before them were like those of a spectator to make out the ex- 
act structure of a great building which he sees at a distance 
in the dim twilight. He first sees that the building is really 
there, and sketches out what he believes to be its outlines. As 
the light increases, he finds that his first outline bears but a 
rude resemblance to what now seems to be the real form, and 
he corrects it accordingly. In his first attempts to fill in the 
columns, pilasters, windows, and doors, he mistakes the darker 
shades between the columns for windows, other lighter shad- 
ows for doors, and the pilasters for columns. Notwithstand- 
ing such mistakes, his representation is to a certain extent cor- 
rect, and he will seldom fall into egregious error. The suc- 
cessive improvements in his sketch, from the first rough out- 
line to the finished picture, do not consist in effacing at each 
step everything he has done, but in correcting it, and filling in 
the details. 

The progress of our knowledge of nature is generally of this 
character. But in the case now before us, so great is the dis- 
tance, so dim the light, and so slender our ideas of the princi- 
ples on which the vast fabric is constructed, that we cannot 
pass beyond a few rough outlines. Still there are a few feat- 
ures which we can describe with a near approach to certainty, 
and others respecting which, though our knowledge is some- 
what vague, we can reach a greater or less degree of proba- 



PROBABLE ARRANGEMENT OF THE VISIBLE UNIVERSE. 487 

bility. We may include these under the following seven 
heads : 

1st. Leaving the nebulae out of consideration, and confining 
ourselves to the stellar system, we may say, with moral cer- 
tainty, that the great mass of the stars which compose this 
system are spread out on all sides, in or near a widely extend- 
ed plane passing through the Milky Way. In other words, 
the large majority of the stars which we can see with the tele- 
scope are contained in a space having the form of a round, flat 
disk, the diameter of which is eight or ten times its thickness. 
This was clearly seen by Kant, and has been confirmed by 
Ilerschel and Strove, In fact, it forms the fundamental base 
of the structures reared by these several investigators. When 
Kant saw, in this arrangement, a resemblance to the solar 
system, in which the planets all move round near one central 
plane, he was correct, so far as he went. The space, then, in 
which we find most of the stars to be contained is bounded 
by two parallel planes forming the upper and lower surfaces 
of the disk we have described, the distance apart of these 
planes being a small fraction of their extent — probably less 
than an eighth. 

2d. Within the space we have described the stars are not 
scattered uniformly, but are for the most part collected into 
irregular clusters or masses, with comparatively vacant spaces 
between them. These collections have generally no definite 
boundaries, but run into each other by insensible gradations. 
The number of stars in each collection may range from two 
to many thousands ; and larger masses are made up of smaller 
ones in every proportion, much as the heavy clouds on a sum- 
mer's day are piled upon each other. 

3d. Our sun, with its attendant planets, is situated near the 
centre of the space we have described, so that we see nearly 
the same number of stars in any two opposite quarters of the 
heavens. 

4th. The six or seven thousand stars around us, which are 
easily seen by the naked eye, are scattered in space with a 
near approach to uniformity, the only exception being local 



488 THE STELLAR UNIVERSE. 

clusters, the component stars of which are few in number and 
pretty widely separated. Such are the Pleiades, Coma Bere- 
nices, and perhaps the principal stars of many other constella- 
tions, which are so widely separated that we do not see any 
connection among them. 

5th. The disk which we have described does not represent 
the form of the stellar system, but only the limits within 
which it is mostly contained. The absence of any definite 
boundary, either to star clusters or the stellar system, and the 
number of comparatively vacant regions here and there among 
the clusters, prevent our assigning any more definite form to 
the system than we could assign to a cloud of dust. The thin 
and widely extended space in which the stars are most thickly 
clustered may, however, be called the galactic region. 

6th. On each side of the galactic region the stars are more 
evenly and thinly scattered, but probably do not extend out to 
a distance at all approaching the extent of the galactic region. 
If they do extend out to an equal distance, they are very few 
in number. It is, however, impossible to set any definite boun- 
daries, not only from our ignorance of the exact distance of 
the smallest stars we can see in the telescope, but because the 
density of the stars probably diminishes very gradually as we 
go out towards the boundary. 

7th. On each side of the galactic and stellar region we have 
a nebular region, in which we find few or no stars, but vast 
numbers of nebulae. The nebulae diminish greatly in num- 
ber as we approach the galactic region, only a very few being 
found in that region. 

The general arrangement of the stars and nebulae which we 
have described is seen in Fig. Ill, which shows what is prob- 
ably the general aspect of a section of the visible universe per- 
pendicular to the Milky Way. In the central part of the fig- 
ure we have the galactic region, in which the stars are mostly 
aggregated in large masses. Of the arrangement of these 
masses nothing certain is known ; they are, therefore, put in 
nearly at random. Indeed, it is still an undecided question 
whether the aggregations of stars which make up the Milky 



PROBABLE ARRANGEMENT OF THE VISIBLE UNIVERSE. 4^0 

Way extend all the way across the diameter of the galactic 
region, or whether they are arranged in the form of a ring, 
with our sun and his surrounding stars in the centre of it. 
In the latter case, the masses of stars near the centre should 
be less strongly marked. This central region being that in 
which our earth is situated, this uncertainty respecting the 
density of stars in that region implies an uncertainty whether 




Fig. 111.— Probable arrangement of the stars and nebulae visible with the telescope. In 
the Galaxy the stars are not evenly scattered, but are agglomerated into clusters. 

the stars visible with the naked eye are part of one of the 
masses which make up the Galaxy, or whether we are in a 
comparatively thin region. Although this question is still 
unsolved, it is one which admits of an answer by telescopic 
research. When we described Sir William Herschel's ar- 
rangement of the stars in concentric spheres, we saw that in 
the more distant spheres the stars were vastly more dense 



490 TEE STELLAR UNIVERSE. 

around the galactic belt of each sphere than they were in 
other parts of it. To answer the question which has been 
presented, we must compare the densities of the stars at the 
circumferences of these spheres with the density immediately 
around us. In other words, the question is, Suppose a human 
being could dart out in the direction of the Milky Way, and 
pass through some of the masses of stars composing it, would 
he find them thicker or thinner than they are in the visible 
heavens around us ? 

A question still left open is, whether all the celestial objects 
visible with the telescope are included within the limits of the 
three regions we have jnst indicated, or whether the whole 
Galaxy, with everything which is included within its limits, 
is simply one of a great number of widely scattered stellar 
systems. Since any consideration of invisible galaxies and 
systems would be entirely idle, the question may be reduced 
to this : Are the most distant star clusters which the telescope 
shows ns situated within the limits of the stellar system or far 
without them, a great vacant space intervening? The latter 
alternative is the popular one, first suggested by Kant, it be- 
ing supposed that the most distant nebulae constituted other 
Milky Ways or stellar systems as extensive as our own. 

Although the possibility that this view is correct cannot be 
denied, yet the arrangement of the star clusters or resolvable 
nebulae militates against it. We have shown that the major- 
ity of the latter lie near the direction of the plane of the 
Milky Way, comparatively few being seen near the perpen- 
dicular direction. But if these objects were other galaxies, 
far outside of the one which snrrounds us, they would be as 
likely to lie in one direction as in another, and the probabil- 
ity against the great mass of them lying in one plane would 
be very great. The most probable conclusion, therefore, is 
that they constitute part of our stellar system. They may, in- 
deed, be scattered around or outside of the extreme limits with- 
in which single stars can be seen, but not at distances so great 
that they should be considered as separate systems. The most 
probable conclusion, in the present state of our knowledge, 






DO THE STARS HE ALLY FORM A- SYSTEM f 401 

seems to be that the scheme shown in Fig. Ill include- the 
whole visible universe. 

The differences of opinion which now exist respecting the 
probable arrangement and distance of the stars arise mainly 
from our uncertainty as to what is the probable range of ab- 
solute magnitude of the stars, a subject to which we have al- 
ready several times alluded. The discovery of the parallax 
of several stars has enabled us not only to form some idea of 
this question by comparing the brilliancy of these stars with 
their known distances, but it has enabled us to answer the in- 
teresting question, How does our sun compare with these stars 
in brightness? The curious result of this inquiry is, that our 
sun is really a star less than the average, which would mod- 
estly twinkle among the smaller of its fellows if removed 
to the distance from us at which they are placed. Zullner 
found, by comparing the light of the sun with that of Capella, 
or a Auriga?, that it would have to be removed to 236,000 
times its present distance to appear equally bright with that 
star, which we may take as an average star of the first magni- 
tude. But the greater number of the stars of this magnitude 
are situated at four or rive times this distance; so that if our 
sun were placed at their average distance, v it would probably 
not exceed the third or fourth magnitude. Still, it would by 
no means belong among the smallest stars of all, because we 
do find stars with a measurable parallax which are only of 
the fifth, sixth, or even the seventh magnitude. Altogether, it 
appears that the range of absolute brilliancy among the stars 
extends through eisrht or ten magnitudes, and that the largest 
ones emit several thousand times as much light as the small- 
est. It is this range of magnitude which really forms the 
greatest obstacle in the way of determining the arrangement 
of the stars in space. 

§ 4. Do the Stars really form a System? 

We have described the sublime ideas of Kant and Lam- 
bert, who, seeing the bodies of our solar system fitted to go 
through their revolutions without permanent change during 



492 



THE STELLAR UNIVERSE. 



an indefinite period of time, reasoned by analogy that the 
stellar universe was constructed on the same general plan, 
and that each star had its appointed orbit, round which it 
would run its course during endless ages. This speculation 
was not followed up by Herschel and Struve, who, proceeding 
on a more strictly scientific plan, found it necessary to learn 
how the stars are now situated before attempting to decide 
in what kinds of orbits they are moving. In the absence of 
exact knowledge respecting the structure and extent of the 
stellar system, it is impossible to say with certainty what will 
be the state of that system after the lapse of the millions of 
years which would be necessary for the stars to perform a 
revolution around one centre. But, as in describing the con- 
stitution of the stellar system, we found certain features on 
which we could pronounce with a high degree of probability, 
so, in respect to the motions and orbits of the stars, there are 
some propositions which we may sustain with a near approach 
to certainty. 

Stability of the System.— We may first assert, with a high de- 
gree of probability, that the stars do not form a stable system 
in the sense in which we say that the solar system is stable. 
By a stable system we mean one in which each star moves 
round and round in an unchanging orbit, every revolution 
bringing it back to its starting-point, so that the system as a 
whole shall retain the same general form, dimensions, and 
arrangement during innumerable revolutions of the bodies 
which compose it. It is almost necessary to the existence of 
such a system that it have a great central body, the mass of 
which should be at least vastly greater than that of the indi- 
vidual bodies which revolve around it. At least, such a cen- 
tral body could be dispensed with only by the separate stars 
having a regularity of motion and arrangement which cer- 
tainly does not exist in the stellar system as we actually see 
it. The question, then, reduces itself to this : Are there any 
immense attracting centres around which the separate collec- 
tions of stars revolve ; or is there any centre around which all 
the stars which compose the visible universe revolve \ In all 



DO THE STABS REALLY FORM A SYSTEM f 493 

human probability, these questions must be answered in the 
negative. All analogy leads us to believe that if there were 
any such central masses, they would be not only larger than 
the other stars, but brighter in a yet greater proportion. It 
is, of course, possible to conceive of immense dark bodies, 
such as Lambert supposed to exist, but we cannot but believe 
the existence of such bodies to be very improbable. Al- 
though there is, as we have seen, great diversity among the 
stars in respect to their magnitudes, there are none of them 
which seem to have that commanding preeminence above 
their fellows which the sun presents above the planets which 
surround him. 

But the most conclusive proof that the stars do not revolve 
round definite attracting centres is found in the variety and 
irregularity of their proper motions, which we have already 
described. We have shown (1) that when the motions of 
great numbers of stars are averaged, there is found a general 
preponderance of motions from the constellation Hercules, 
which is supposed to be due to a motion of our sun with his 
attendant planets in that direction ; and (2) that when the 
motions of stars in the same region are compared, there is 
often found to be a certain resemblance among them. Bnt 
this tendency towards a regular law affects only large masses 
of stars, and does not imply any such regularity in the mo- 
tions of individual stars as would be apparent if they moved 
in regular circular orbits, as the planets move round the sun. 
The motion of each individual star is generally so entirely 
different from that of its fellows as seemingly to preclude all 
reasonable probability that these bodies are revolving in defi- 
nite orbits around great centres of attraction. 

The most extraordinary instances of the irregularities of 
which we speak are found in the stars of unusually rapid 
proper motion, which are moving forward at such a rate that 
the gravitation of all the known stars cannot stop them until 
they shall have passed through and beyond the visible uni- 
verse. The most remarkable of these, so far as we know, is 
Groombridge 1830, it having the largest apparent proper mo- 



494 THE STELLAR UNIVERSE. 

tion of any known star. The most careful determinations of 
its parallax seem to show that its distance is so immense that 
the parallax is only about a tenth of a second ; that is, a line 
drawn from the sun to the earth would subtend an an^le of 
only a tenth of a second when viewed from this star. But 
the apparent motion of the star, as we actually see it, is more 
than seven seconds per annum, or seventy times its parallax. 
It follows that the star moves over a space of more than sev- 
enty times the distance of the sun from us in the space of a 
year. If, as is likely, the motion of the star is oblique to the 
line in which we see it, its actual velocity must be yet greater. 
Leaving this out of account, we see that the star would pass 
from the earth to the sun in about five days, so that its veloci- 
ty probably exceeds two hundred miles per second. 

To understand what this enormous velocity may imply, we 
must advert to the theorem of gravitational astronomy that 
the velocity which a body can acquire by falling towards an 
attracting centre is, at each point of its path, limited. For ex- 
ample, a body falling from an infinite distance to the earth's 
surface, and acted on by the attraction of the earth alone, would 
acquire a velocity of only about seven miles per second. Vice 
versa,& body projected from the earth with this velocity would 
never be stopped by the earth's attraction alone, but would 
describe an elliptic orbit round the sun. If the velocity ex- 
ceeded twenty-seven miles per second, the attraction of the sun 
himself could never stop it, and it would wander forever 
through the stellar spaces. The greater the distance from the 
sun at which the body is started, the less the velocity which 
will thus carry it forever away from the sun. At the orbit of 
Uranus the required velocity would be only six miles per sec- 
ond ; at Neptune, it would be less than five miles per second ; 
half-way between the sun and a Centauri, it would be a mile 
in twelve seconds, or a fourth the speed of a cannon-ball. If 
we knew the masses of each of the stars, and their arrange- 
ment in space, it would be easy to compute this limiting ve- 
locity for a body falling from an infinite distance to any point 
of the stellar system. If the motion of a star were found to 



DO THE STARS REALLY FORM A SYSTEM? 495 

exceed this limit, it would show that the star did not belong 

to the visible universe at all, but was only a visitor flying 
on a course through infinite space at such a rate that the 
combined attraction of all the stars could never stop it. 

Let us now see how the case may stand with our flying star, 
and what relation its velocity may bear to the probable attrac- 
tion of all the stars which exist within the range of the tel- 
escope. The number of stars actually visible with the m 
powerful telescopes probably falls short of fifty millions; but, 
to take a probable outside limit, we shall suppose that within 
the regions occupied by the farthest stars which the telescope 
will show, there are fifty millions more, so small that we cannot 
see them, making one hundred millions in all. We shall also 
suppose that these stars have, on the average, five times the 
mass of the sun, and that they are spread out in a layer across 
the diameter of which light would require thirty thousand years 
to pass. Then, a mathematical computation of the attractive 
power exerted by such a system of masses shows that a body 
falling from an infinite distance to the centre of the system 
would accpiire a velocity of twenty -five miles per second. 
Vice versa, a body projected from the centre of such a system 
with a velocity of more than twenty-five miles per second in 
any direction whatever would not only pass entirely through 
it, but would fly off into infinite space, never to return. If the 
body were anywhere else than in the centre of the system, the 
velocity necessary to carry it away would be less than the 
limit just given. But this calculated limit is only one-eighth 
the probable velocity of 1830 Groombridge. The force re- 
quired to impress a given velocity on a body falling through 
any distance is proportional to the square of the velocity, four 
times the force being required to give double the velocity, nine 
times to increase it threefold, and so on. To give eight times 
the velocity would require sixty-four times the attracting mass. 
If, then, the star in question belongs to our stellar system, the 
masses or extent of that system must be many times greater 
than telescopic observation and astronomical research indicate. 
We may place the dilemma in a concise form, as follows: 

33 



490 THE STELLAR UNIVERSE '. 

Either the bodies which compose our universe are vastly 
more massive and numerous than telescopic examination 
seems to indicate, or 1830 Groombridge is a runaway star, 
flying on a boundless course through infinite space with such 
momentum that the attraction of all the bodies of the universe 
can never stop it. 

Which of these is the more probable alternative we cannot 
pretend to say. That the star can neither be stopped, nor bent . 
far from its course until it has passed the extreme limit to 
which the telescope has ever penetrated, we may consider 
reasonably certain. To do this will require two or three mill- 
ions of years. Whether it will then be acted on by attractive 
forces of which science has no knowledge, and thus carried 
back to. where it started, or whether it will continue straight 
forward forever, it is impossible to say. 

Much the same dilemma may be applied to the past history 
of this body. If the velocity of two hundred miles or more 
per second with which it is moving exceeds any that could be 
produced by the attraction of all the other bodies in the uni- 
verse, then it must have been flying forward through space 
from the beginning, and, having come from an infinite dis- 
tance, must be now passing through our system for the first 
and only time. 

It may be asked whether, in Lambert's hypothesis of im- 
mense attracting bodies, invisible on account of their being 
dark, we have not at once the centres required to give general 
stability to the stellar system, and to keep the star of which 
we have spoken in some regular orbit. We answer, no. To 
secure such stability, stars equally distant from the attracting 
centres must move with nearly the same velocity. An at- 
tracting centre sufficiently powerful to bring a body moving 
two hundred miles per second into a regular orbit would 
draw most of the other stars moving with small velocities into 
its immediate neighborhood, and thus subvert the system. We 
thus meet the double difficulty that we have good reason to 
doubt the existence of these opaque, dark bodies, and that if 
they did exist, they would not fulfil our requirements. 



DO THE STARS REALLY FORM A SYSTEM f 41 > 7 

The general result of our inquiry is that the stellar uni- 
verse does not seem to possess that form of unvarying stabil- 
ity which we see in the solar system, and that the stars move 
in irregular courses depending on their situation in respect 
to the surrounding stars, and probably changing as this situa- 
tion changes. If there were no motion at all among the star-. 
they would all fall to a common centre, and universal ruin 
would be the result. But the motions which we actually 
are sufficient to prevent this catastrophe, by supplying each 
star with a reserve of force which will generally keep it from 
actual collision with its neighbors. If, then, any one star 
does fall towards any attracting centre, the velocity which it 
acquires by this fall will carry it away again in some other 
direction, and thus it may keep up a continuous dance, under 
the influence of ever-varying forces, as long as the universe 
shall exist under its present form. 

To those who have been enraptured with the sublime specu- 
lations of Kant and Lambert, this may seem an unsatisfactory 
conclusion; while to those who look upon the material uni- 
verse as something made to last forever, it may seem improba- 
ble. But when we consider the immense periods which would 
be required for the mutual gravitation of the stars to effect 
any great change in the stellar system, we may be led to alter 
such views as these. We have shown that tens of thousands 
of years would be required to make any great change in the 
arrangement of the stars which we see with the naked eye. 
The time required for all the stars visible with the telescope 
to fall together by their own attraction is to be counted by 
millions of years. If the universe had existed in its present 
state from eternity, and were to exist forever, the immensity 
of these periods would not be at all to the point, because a 
million of years is no more a part of eternity than a single 
day. But all modern science seems to point to the Unite 
duration of our system in its present form, and to carry us 
back to the time when neither sun nor planet existed, save as 
a mass of glowing gas. How far back that was, it cannot tell 
us with certainty ; it can only say that the period is counted 



498 THE STELLAR UNIVERSE. 

by millions of years, but probably not by hundreds of mill- 
ions. It also points forward to the time when the sun and 
stars shall fade away, and nature shall be enshrouded in dark- 
ness and death, unless some power now unseen shall uphold 
or restore her. The time required for this catastrophe cannot 
be calculated ; but it is probaoly not so great that the stellar 
system can, in the mean time, be subverted by the mutual 
gravitation of its members. 

It would thus appear as if those nicely arranged adjust- 
ments which secure stability and uniformity of motion are 
not found where they are not necessary to secure the system 
from subversion during the time it is to last, much as the 
wheel of an engine which is to make but two or three revo- 
lutions while the engine endures need not be adjusted to 
make thousands of revolutions. The bodies which form our 
solar system are, on the other hand, like wheels which have 
to make millions of revolutions before they stop. Unless there 
is a constant balance between the opposing forces under the 
influence of which they move, there must be a disarrangement 
of the movement long before the engine wears out. Thus, 
although the present arrangement of the stars may be studied 
without any reference to their origin, yet, when we seek to 
penetrate the laws of their motion, and foresee the changes 
of state to which their motions may give rise, we are brought 
to face the question of their duration, and hence of their be- 
ginning and end. 






THE COSMOGONY 499 



CHAPTER III. 



THE COSMOGONY. 



The idea that the world has not endured forever in the 
form in which we now see it, but that there was a time when 
it either did not exist at all, or existed only as a mass "with- 
out form, and void," is one which we lind to have been always 
held by mankind. The "chaos" of the Greeks — the rude and 
formless materials, subject to no law, out of which all things 
were formed by the creative power — corresponds in a striking 
manner to the nebulous masses of modern astronomy. These 
old ideas of chaos were expressed by Milton in the second 
book of " Paradise Lost," before such a thing as a nebula 
could be said to be known-, and he would be a bold astrono- 
mer who, in giving a description of the primeval nebulous 
mass, would attempt to improve on the great poet : 

"a dark, 

Illimitable ocean, without bound, 

Without dimension, where length, breadth, and height, 

And time and place, are lost : where eldest Night 

And Chaos, ancestors of Nature, hold 

Eternal anarchy amidst the noise 

Of endless wars, and by confusion stand: 

For hot, cold, moist, and dry, four champions tierce, 

Strive here for mastery, and to battle bring 

Their embryon atoms. 

* * * * * * * 

Chaos umpire sit>. 
And by decision more embroils the fray 
By which he reigns : next him, high arbiter, 
Chance governs all. Into this wild abyss 
The womb of Nature, and perhaps her grave, 
Of neither sea, nor shore, nor air, nor fire, 
But all these in their pregnant causes mixed 
Confusedly, and which thus must ever light, 



500 THE STELLAR UNIVERSE. 

Unless the almighty Maker them ordain 
His dark materials to create more worlds — 
* * * * * * . 

Some tumultuous cloud 
Instinct with fire and nitre." 

If we classify men's ideas of the cosmogony according to 
the data on which they are founded, we shall find them divis- 
ible into three classes. The first class comprises those formed 
before the discovery of the theory of gravitation, and which, 
for this reason, however correct they might have been, had no 
really scientific foundation. The second are those founded on 
the doctrine of gravitation, but without a knowledge of the 
modern theory of the conservation of force ; while the third 
are founded on this theory. It must not be supposed, how- 
ever, that the ideas of the last-mentioned class are antagonistic 
to those of the other classes. Kant and Laplace founded the 
nebular hypothesis on the theory of gravitation alone, the con- 
servation of force being then entirely unknown. It was, there- 
fore, incomplete as it came from- their hands, but not neces- 
sarily erroneous in its fundamental conceptions. 

The consideration of the ancient ideas of the origin of the 
world belongs rather to the history of philosophy than to as- 
tronomy, for the reason that they were of necessity purely 
speculative, and reflected rather the mode of thought of the 
minds in which they originated than any definite system of 
investigating the operations of nature. The Hindoo concep- 
tion of Brahma sitting in meditation on a lotus-leaf through 
long ages, and then producing a golden egg as large as the 
universe, out of which the latter was slowly evolved, is not 
founded on even the crudest observation, but is purely a result 
of the speculative' tendency of the Hindoo mind. The Jew- 
ish cosmogony is the expression of the monotheistic views of 
that people, and of the identity of their tutelary divinity with 
the maker of heaven and earth. Hipparchus and Ptolemy 
showed the scientific turn of their minds by confining them- 
selves to the examination of the universe as it is, without mak- 
ing any vain effort to trace its origin. 



THE MODERN NEBULAR HYPOTHESIS. 501 

Though the systems to which we refer are essentially un- 
scientific, it must not be supposed that they were all errone- 
ous in their results, or that they belong exclusively to ancient 
times. Thus, the views of Swedenborg, though they belong 
to the class in question, are remarkably in accordance with 
recent views of the subject as regards the actual changes which 
took place during the formation of the planets. A great deal 
of what is written on the subject at present is to be included 
in this same ancient class, as being the production of men who 
are not mathematicians or working astronomers, and who, 
therefore, cannot judge whether their views are in accordance 
with mechanical laws and with the facts of observation. Pass- 
ing over all speculation of this sort, no matter when or by 
whom produced, we shall consider in historical order the works 
of those who have actually contributed to placing the laws of 
cosmogony on a scientific foundation. 

§ 1. The Modern Nebular Hypothesis. 

From a purely scientific point of view, Kant has probably 
the best right to be regarded as the founder of the nebular 
hypothesis, because he based it on an examination of the actual 
features of the solar system, and on the Newtonian doctrine 
of the mutual gravitation of all matter. His reasoning is 
briefly this: Examining the solar system, we find two remark- 
able features presented to our consideration. One is that six 
planets and nine satellites (the entire number then known) 
move around the sun in circles, not only in the same direction 
in which the sun himself revolves on his axis, but very nearly 
in the same plane. This common feature of the motion of 
so many bodies could not, by any reasonable possibility, have 
been a result of chance ; we are, therefore, forced to believe 
that it must be the result of some common cause originally 
acting on all the planets. 

On the other hand, when we consider the spaces in which 
the planets move, we find them entirely void, or as good as 
void ; for if there is any matter in them, it is so rare as to be 
without effect on the planetary motions. There is, therefore, 



502 THE STELLAR UNIVERSE. 

no material connection now existing between the planets 
through which they might have been forced to take up a com- 
mon direction of motion. How, then, are we to reconcile this 
common motion with the absence of all material connection ? 
The most natural way is to suppose that there was once some 
such connection which brought about the uniformity of mo- 
tion which we observe ; that the materials of which the plan- 
ets are formed once filled the whole space between them. " I 
assume," says Kant, " that all the materials out of which the 
bodies of our solar system were formed were, in the begin- 
ning of things, resolved in their original elements, and filled all 
the space of the universe in which these bodies now move/' 
There was no formation in this chaos, the formation of sepa- 
rate bodies by the mutual gravitation of parts of the mass be- 
ing a later occurrence. But, naturally, some parts of the mass 
would be more dense than others, and would thus gather 
around them the rare matter which filled the intervening 
spaces. The larger collections thus formed would draw the 
smaller ones into them, and this process would continue until 
a few round bodies had taken the place of the original chaotic 
mass. 

If we examine the result of this hypothesis by the light of 
modern science, we shall readily see that all the bodies thus 
formed would be drawn to a common centre, and thus we 
should have, not a collection of bodies like the solar system, 
but a single sun formed by the combination of them all. In 
attempting to show how the smaller masses would be led to 
circulate around the larger ones in circular orbits, Kant's rea- 
soning ceases to be satisfactory. He seems to think that the 
motion of rotation could be produced indirectly by the repul- 
sive forces acting among the rarer masses of the condensing 
matter, which would give rise to a whirling motion. But the 
laws of mechanics show that the sum total of rotary motion in 
a system can never be increased or diminished by the mutual 
action of its separate parts, so that the present rotary motions 
of the sun and planets must be the equivalent of that which 
they had from the beginning. 



THE MODERN NEBULAR HYPOTHESIS. 503 

HerscheVs Hypothesis. — It is remarkable that tire idea of 
the gradual transmutation of nebulae into stars seems to have 
been suggested to Herschel, not by the relations of the solar 
system, but by his examinations of the nebulae themselves. 
Many of these bodies seemed to him to be composed of im- 
mense masses of phosphorescent vapor, and he conceived that 
these masses must be gradually condensing, each around its 
own centre, or around those parts where it is most dense, until 
it should be transmuted into a star or a cluster of stars. ( )n 
classifying the numerous nebulae which he discovered, it 
seemed to him that he could see each stage of this operation 
going on before his eyes. There were the large, faint, diffused 
nebulae, in which the process of condensation seemed to have 
hardly begun; the smaller but brighter ones, which had been 
so far condensed that the central parts would soon begin to 
form into stars; yet others, in which stars had actually begun 
to form ; and, finally, star clusters in which the condensation 
was complete. As Laplace observes, Herschel followed the 
condensation of the nebulae in much the same way that we 
can, in a forest, study the growth of the trees by comparing 
those of the different ages which the forest contains at the 
same time. The spectroscopic revelations of the gaseous nat- 
ure of the true nebulae tend to strengthen these views of Her- 
schel, and to confirm us in the opinion that these masses will 
all at some time condense into stars or clusters of stars. 

Laplace s View of th< Nebular Hypothesis. — Laplace was led 
to the nebular hypothesis by considerations very similar to 
those presented by Kant a few years before. The remarkable 
uniformity among the directions of rotation of the planets be- 
ing: something which could not have been the result of chance, 
he sought to investigate its probable cause. This cause, he 
thought, could be nothing else than the atmosphere of the sun, 
which once extended so far out as to fill all the space now oc- 
cupied by the planets. He does not, like. Kant, begin with a 
chaos, out of which order was slowly evolved by the play of 
attractive and repulsive forces, but with the sun, surrounded 
by this immense fiery atmosphere. Knowing, from mechan- 



504 THE STELLAR UNIVERSE. 

ical laws, that the sum total of rotary motion now seen in the 
planetary system must have been there from the beginning, he 
conceives the immense vaporous mass forming the sun and 
his atmosphere to have had a slow rotation on its axis. The 
mass being intensely hot would slowly cool off, and as it did so 
would contract towards the centre. As it contracted, its ve- 
locity of rotation would, in obedience to one of the funda- 
mental laws of mechanics, constantly increase, so that a time 
would arrive when, at the outer boundary of the mass, the cen- 
trifugal force due to the rotation would counterbalance the at- 
tractive force of the central mass. Then, those outer portions 
would be left behind as a revolving ring, while the next inner 
portions would continue to contract until, at their boundary, 
the centrifugal and attractive forces would be again balanced, 
when a second ring would be left behind, and so on. Thus, 
instead of a continuous atmosphere, the sun would be sur- 
rounded by a series of concentric revolving rings of vapor. 

Now, how would these rings of vapor behave ? As they 
cooled off, their denser materials would condense first, and 
thus the ring would be composed of a mixed mass, partly solid 
and partly vaporous, the quantity of solid matter constantly 
increasing, and that of vapor diminishing. If the ring were 
perfectly uniform, this condensing process would take place 
equally all around it, and the ring would thits be broken up 
into a group of small planets, like that which we see between 
Mars and Jupiter. But we should expect that in general 
some portions of the ring would be much denser than others, 
and the denser portions would gradually attract the rarer por- 
tions around it until, instead of a ring, we should have a sin- 
gle mass, composed of a nearly solid centre surrounded by an 
immense atmosphere of fiery vapor. This condensation of the 
ring of vapor around a single point would have produced no 
change in the amount of rotary motion originally existing in 
the ring ; the planet, surrounded by its fiery atmosphere, would 
therefore be in rotation, and would be, in miniature, a repro- 
duction of the case of the sun surrounded by his atmosphere 
with which we set out. In the same way that the solar at- 



THE MODERN NEBULAR HYPOTHESIS. 505 

mosphere formed itself first into rings, and then these rings 
condensed into planets, so, if the planetary atmospheres were 
sufficiently extensive, they would form themselves into rings, 
and these rings would condense into satellites. In the case of 
Saturn, however, one of the rings was so perfectly uniform 
that there could be no denser portion to draw the rest of 
the ring around it, and thus we have the well-known rings 
of Saturn. 

If, among the materials of the solar atmosphere, there were 
any so rare and volatile that they would not unite themselves 
either into a ring or around a planet, they would continue t<» 
revolve around the sun, presenting an appearance like that 
of the zodiacal light. They would offer no appreciable re- 
sistance to the motion of the planets, not only on account of 
their extreme rarity, but because their motion would be the 
same as that of the planets which move among them. 

Such is the celebrated nebular hypothesis of Laplace which 
has given rise to so much discussion. It commences, not with 
a purely nebulous mass, but with the sun surrounded by a 
fiery atmosphere, out of which the planets were formed. On 
this theory the sun is older than the planets; otherwise it 
would have been impossible to account for the slow rotation 
of the sun upon his axis. If his body had been formed of ho- 
mogeneous matter extending out uniformly to near the orbit 
of Mercury, it would not have condensed into a globe revolv- 
ing on its axis in twenty-five days, but into a flat, almost lens- 
shaped, body, which would have been kept from forming a 
sphere by the centrifugal force. But the denser materials be- 
ing condensed first, perhaps into such a body as we described, 
the friction of the uncondensed atmosphere would have di- 
minished the rotation of the sun, the rotating energy which he 
lost being communicated to the embryo planets and throwing 
them farther away. 

In accordance with the hypothesis of Laplace, it has al- 
ways been supposed that the outer planets were formed first. 
There is, however, a weak point in Laplace's theory of the for- 
mation of rings. He supposed that when the centrifugal and 



506 THE STELLAR UNIVERSE. 

centripetal forces balanced each other at the outer limit of 
the revolving mass, the outer portions were separated from the 
rest, which continued to drop towards the centre. If the plan- 
etary rings were formed in this way, then, after each ring was 
thrown off, the atmosphere must have condensed to nearly 
half its diameter before another would have been thrown off, 
because we see that each planet is, on the whole, nearly twice 
as far as the one next within it. But there being no cohe- 
sion between particles of vapor, such thro wing-off of immense 
masses of the outside portions of the revolving mass was im- 
possible. The moment the forces balanced, the outer portions 
of the mass would, indeed, cease to drop towards the sun, and 
would partially separate from the portions next to it ; then 
these would separate next, and so on ; that is, there would be 
a constant dropping-off of matter from the outer portions, so 
that, instead of a series of rings, there would have been a flat 
disk formed of an infinite number of concentrating rings all 
joined together. 

If we examine the subject more closely, we shall see that 
the whole reasoning by which it is supposed that the inner 
portions of the mass would drop away from the outer ones 
needs important modifications. In its primeval state, when it 
extended far beyond the present confines of the solar system, 
the rare nebulous atmosphere must have been nearly spherical. 
As it gradually contracted, and the effect of centrifugal force 
thus became more marked, it would have assumed the form 
of an oblate spheroid. When the contraction had gone so 
far that the centrifugal and attracting forces nearly balanced 
each other at the outer equatorial limit of the mass, the result 
would have been that contraction in the direction of the equa- 
tor would cease entirely, and be confined to the polar regions, 
each particle dropping, not towards the sun, but towards the 
plane of the solar equator. Thus, we should have a constant 
flattening of the spheroidal atmosphere until it was reduced 
to a thin flat disk. This disk might then separate itself into 
rings, which would form planets in much the same way that 
Laplace supposed. But there would probably be no marked 



PROGRESSIVE CHANGES IN OUR SYSTEM. 507 

difference in the age of the planets; quite likely the smaller 
inner rings would condense into planets more rapidly than the 
wide-spread outer ones. 

Kant and Laplace may be said to have arrived at the neb- 
ular hypothesis by reasoning forward, and showing how, by 
supposing that the space now occupied by the solar system 
was once filled by a chaotic or vaporous mass, from which the 
planets were formed, the features presented by this system 
could be accounted for. We are now to show how our mod- 
ern science reaches a similar result by reasoning backward 
from actions which we see going on before our eyes. 

§ 2. Progressive Changes in our System. 

During the short period within which accurate observations 
have been made, no actual permanent change has been ob- 
served in our system. The earth, sun, and planets remain of 
the same magnitude, and present the same appearance as al- 
ways. The stars retain their brilliancy, and, for the most part, 
the nebulae their form. Not the slightest variation has been 
detected in the amount of heat received from the sun, or in 
the average number and extent of the spots on his surface. 
And yet we have reason to believe that these things are all 
changing, and that the time will come when the state of the 
universe will be very different from that in which we now see 
it. How a change may be inferred when none is actually vis- 
ible may be shown by a simple example. 

Suppose an inquiring person, walking in what he sup- 
posed to be a deserted building, to find a clock running. If 
he is ignorant of mechanics, he will see no reason why it may 
not have been running just as he now sees it for an indefinite 
period, and why the pendulum may not continue to vibrate, 
and the hands to go through their revolutions, so long as the 
fabric shall stand. He sees a continuous cycle of motions, and 
can give no reason why they should not have been going on 
since the clock was erected, arid continue to go on till it shall 
decay. But let him be instructed in the laws of mechanics, 
and let him inquire into the force which keeps the hands and 



508 THE STELLAR UNIVERSE. 

pendulum in motion. He will then find that this force is 
transmitted to the pendulum through a train of wheels, each 
of which moves many times slower than that in front of it, 
and that the first wheel is acted upon by a weight, with which 
it is connected by a cord. He can see a slow motion in the 
wheel which acts on the pendulum, and perhaps in the one 
next behind it, while during the short time he has for exami- 
nation he can see no motion in the others. But if he sees how 
the wheels act on each other, he will know that they must all 
be in motion ; and when he traces the motion back to the first 
wheel, he sees that its motion must be kept up by a gradual 
falling of the weight, though it seems to remain in the same 
position. He can then say with entire certainty: "I do not see 
this weight move, but I know it must be gradually approach- 
ing the bottom, because I see a system of moving machinery, 
the progress of which necessarily involves such a slow falling 
of the weight. Knowing the number of teeth in each wheel 
and pinion, I can compute how many inches it falls each day ; 
and seeing how much room it has to fall in, I can tell how 
many days it will take to reach the bottom. When this is 
done, I see that the clock must stop, because it is only the fall- 
ing of the weight that keeps its pendulum in motion. More- 
over, I see that the weight must have been higher yesterday 
than it is to-day, and yet higher the day before, so that I can 
calculate its position backward as well as forward. By this 
calculation I see backward to a time when the weight was 
at the top of its course, higher than which it could not be. 
Thus, although I see no motion, I see with the eye of reason 
thai the weight is running through a certain course from the 
top of the clock to the bottom ; that some power must have 
wound it up and started it; and that unless the same power 
intervenes again, the weight must reach the bottom in a cer- 
tain number of days, and the clock must then stop." 

The corresponding progressive change exhibited by the 
operations of nature consists in a constant transformation of 
motion into heat, and the constant loss of that heat by radia- 
tion into space. As Sir William Thomson has expressed it, 



PROGRESSIVE CHANGES IN 01 11 SYSTEM. 509 

a constant "dissipation of energy " is going on in nature. 
We all know that the sun has been radiating heat into space 
during the whole course of his existence. A small portion of 
this heat strikes the earth, and supports life and motion on its 
surface. All this portion of the sun's heat, after performing 
its function, is radiated off into space by the earth itself. The 
portion of the sun's radiant heat received by the earth is. how- 
ever, comparatively insignificant, since our luminary radiates 
in every direction equally, while the earth can receive only a 
part represented by the ratio which its apparent angular mag- 
nitude as seen from the sun bears to the whole celestial sphere, 
which a simple calculation shows to be the ratio of 1 to 
L', 170,000,000. The star.- radiate heat as well as the sun. 
The heat received from them, when condensed in the focus of 
a telescope, has been rendered sensible by the thermo-multi- 
plier, and there is every reason to believe that stellar heat and 
light bear the same proportion to each other that solar heat 
and light do. Wherever there is white stellar light, there 
must be stellar heat; and as we have found that the stars in 
general give more light than the sun, we have reason to be- 
lieve that they give more heat also. Thus we have a contin- 
uous radiation from all the visible bodies of the universe, 
which must have been croino; on from the bearinnincj. 

Until quite recently, it was not known that this radiation 
involved the expenditure of a something necessarily limited in 
supply, and, consequently, it was not known but that it might 
continue forever without any loss of power on the part of the 
sun and stars. But it is now known that heat cannot be pro- 
duced except by the expenditure of force, actual or potential, 
in some of its forms, and it is also known that the available 
supply of force is necessarily limited. One of the best-estab- 
lished doctrines of modern science is that force can no more 
be produced from nothing than matter can: to find it so pro- 
duced would be as complete a miracle as to see a globe created 
from nothing before our eyes. Hence, this radiation cannot 
go on forever unless the force expended in producing the heat 
be returned to the sun in some form. That it is not now 



510 THE STELLAR UNIVERSE. 

so returned we may regard as morally certain. There is no 
known law of radiation , except that it proceeds out in straight 
lines from the radiating centre. If the heat were returned 
back to the sun from space, it would have to return to the 
centre from all directions ; the earth would then intercept as 
much of the incoming as of the outgoing heat ; that is, we 
should receive as much heat from the sky at night as from 
the sun by day. We know very well that this is not the case ; 
indeed, there is no evidence of any heat at all reaching us from 
space except what is radiated from the stars. 

Since, then, the solar heat does not now return to the sun, 
we have to inquire what becomes of it, and whether a com- 
pensation may not at some time be effected whereby all the 
lost heat will be received back again. Now, if we trace the 
radiated heat into the wilds of space, we may make three pos- 
sible hypotheses respecting its ultimate destiny : 

1. We may suppose it to be absolutely annihilated, just as it 
was formerly supposed to be annihilated when it was lost by 
friction. 

2. It may continue its onward course through space forever. 

3. It may, through some agency of which we have no con- 
ception, be ultimately gathered and returned to the sources 
from which it emanated. 

The first of these hypotheses is one which the scientific 
thinkers of the present day would not regard as at all philo- 
sophical. In our scientific philosophy, the doctrine that force 
cannot be annihilated is coequal with that that it cannot be 
created ; and the inductive processes on which the latter doc- 
trine is founded are almost as unimpeachable as those from 
which we conclude that matter cannot be created. At the 
same time, it might be maintained that all these doctrines re- 
specting the uncreatableness and indestructibility of matter 
and force can have no proper foundation except induction 
from experiment, and that the absolute truth of a doctrine 
like this cannot be proved by induction. Especially may this 
be claimed in respect of force. The most careful measures of 
force which we can make under all circumstances show that it 



PROGRESSIVE CHANGES IN OUR SYSTEM. 511 

is subject to no sensible loss by either transmission or transfor- 
mation. But this alone does not prove that it can be subject 
to no loss in a passage through space requiring hundreds of 
thousands or millions of years. There is also this essential 
difference between force and matter, that we conceive the lat- 
ter as made up of individual parts which preserve their iden- 
tity through all the changes of form which they undergo; 
while force is something in which we do not conceive of any 
such identity. Thus, when I allow a drop of water to evapo 
rate from my hand, 1 can in imagination trace each molecule 
of water through the air, into the clouds, and down to the 
earth again in some particular drop of rain, so that, if I only 
had the means of actually tracing it, I could say, "This cup 
contains one, or two, or twenty of the identical molecules 
which evaporated from my hand a week or a month ago." 
It is on this idea of the separate identity of each molecule 
of matter that our opinion of the indestructibility of matter i- 
founded, because matter cannot be destroyed without destroy- 
ing individual molecules, and any cause which could destroy a 
single molecule might equally destroy all the molecules in the 
universe. 

But neither parts nor identity is possible in force. A cer- 
tain amount of heat may be expended in simply raising a 
weight. Here heat has disappeared, and is replaced by a 
mere change of position — something which cannot be con- 
ceived as identical with it. If we let the weight drop, the 
same amount of heat will be reproduced that was expended 
in raising the weight; but, though equal in quantity, it ean- 
not be regarded as identical in the way that the water con- 
densed from steam is identical with that which was evapo- 
rated to form tbe steam. If measures showed it to be less 
in quantity, we could not say there was a destruction of an 
identical something which previously existed, as we could if 
the condensed steam were not equal to the water evaporated. 
Therefore, while the doctrine of the indestructibility of force 
is universally received as a scientific principle, it can hardly 
be claimed that induction has established its absolute correct- 



512 THE STELLAR TJNLVERSE. 

ness; and, in a case like the present, where we see something 
which transcends scientific explanation, the failure of the 
widest induction may be considered among the possible alter- 
natives. 

The second alternative — that the heat radiated from the 
sun and stars continues its onward course through space for- 
ever — is the one most in accord with our scientific concep- 
tions. We actually receive heat from the most distant star 
visible in our telescopes, and this heat has, according to the 
best judgment we can form, been travelling thousands of 
years without any loss whatever. From this point of view, 
every radiation which has ever emanated from the earth or 
the sun is still pursuing its course through the stellar spaces, 
without any other diminution than that which arises from its 
being spread over a wider area. A very striking presentation 
of this view is, we believe, due to some modern writer. If 
an intelligent being had an eye so keen that he could see the 
smallest object by the faintest light, and a movement so rapid 
that he could pass from one bound of the stellar system to the 
other in a few years, then, by viewing the earth from a dis- 
tance much less than that of the farthest star, he would see it 
by light which had left it several thousand years before. By 
simply watching, he would see the whole drama of human his- 
tory acted over again, except where the actions had been hid- 
den by clouds, or under other obstacles to the radiation of light. 
The light from every human action performed under a clear 
sky is still pursuing its course among the stars, and it needs 
only the powers we have mentioned to place a being in front 
of the ray, and let him see the action again. 

If the hypothesis now under consideration be the correct 
one, then the heat radiated by the sun and stars is forever lost 
to them. There is no known way by which the heat thus sent 
off can be returned to the sun. It is all expended in produc- 
ing vibrations in the ethereal medium which constantly ex- 
tend out farther and farther into space. 

The third hypothesis, like the first, is a simple conjecture 
permitted by the necessary imperfection of our knowledge. 



THE SOURCES OF THE SUN'S HEAT. 51o 

All the laws of radiation and all our conceptions of space 
lead to the conclusion that the radiant heat of the sun can 
never he returned to it. Such a return can result only from 
space itself having such a curvature that what seem- to as a 
straight line shall return into itself, as has been imagined by a 
great German mathematician;* or from the ethereal medium, 
the vibrations in which constitute heat being limited in extent : 
or, finally, through some agency as yet totally unknown to 
ence. The first idea is too purely speculative to admit of dis- 
cussion, while the other two suppositions transcend our science 
as completely as does that of an actual annihilation of force. 

§ 3. The Sources of the Sun's Heat. 

We may regard it as good as an observed fact that the sun 
has been radiating heat into void space for thousands or even 
millions of years, without any apparent diminution of the sup- 
ply. One of the most difficult questions of cosmical physics — 
a question the difficulty of which was not seen before the dis- 
covery of the conservation of force — has been, How is this sup- 

* This idea belongs to that transcendental branch of geometry which, rising 
above those conceptions of space derived from our experience, investigates what 
may be possible in the relations of parts of space considered in their widest range. 
It is now conceded that the supposed a priori necessity of the axioms of geom- 
etry has no really sound logical foundation, and that the question of the limita- 
tions within which they are true is one to he settled by experience. Especially i- 
this true of the theorem of parallels, no really valid demonstration either that two 
parallel straight lines will never meet or never diverge being possible. B\ reject- 
ing the limitations imposed upon our fundamental geometrical conceptions, yet 
without admitting anything which positively contradicts them, several geometrical 
systems have been constructed in recent rimes, which are included under the gen- 
eral appellation of the non-Euclidian Geometry. The most celebrated ami re- 
markable of these systems is that of Riemann, who showed that although we are 
obliged to conceive of space as unbounded, since no position is possible which has 
not space on all sides of it, yet there is no necessity that we shall consider it as 
infinite. It may return into itself in something the manner of the surface of a 
sphere, which, though it has no boundary, yet contains only a finite number of 
square feet, and on which one who travels straight forward indefinitely will finally 
arrive at his starting-point. Although this idea of the finitude of space transcends 
our fundamental conceptions, it does not contradict them, and the most that ex- 
perience can tell us in the matter is that, though space be finite, the whole extent 
of the visible universe can be but a very small fraction of the sum total of space. 



514 THE STELLAR UNIVERSE. 

ply of heat kept up? If we calculate at what rate the tem- 
perature of the snu would be lowered annually by the radia- 
tion from its surface, we shall find it to be 2J° Fahrenheit per 
annum, supposing its specific heat to be the same as that of 
water, and from 5° to 10° per annum, if we suppose it the 
same as most of the substances which compose our globe. It 
would, therefore, have entirely cooled off in a few thousand 
years after its formation if it had no other source of heat 
than that shown by its temperature. 

That the temperature could be kept up by combustion, as 
terrestrial fires are kept up, is out of the question, as new fuel 
would have to be constantly added in quantities which cannot 
possibly exist in the neighborhood of the sun. But an allied 
source of heat has been suggested, founded on the law of the 
mechanical equivalency of heat and force. If a body should 
fall into the sun from a great height, all the force of its fall 
would be turned into heat, and the heat thus produced would 
be enormously greater than any that would arise from the 
combustion of the falling body. An instance of this law is 
shown by the passage of shooting-stars and aerolites through 
our atmosphere, where, though the velocity rarely amounts to 
more than forty miles a second, nearly all such bodies are con- 
sumed by the heat generated. Now, the least velocity with 
which a body could strike the sun (unless it had been merely 
thrown from the sun and had fallen back) is about 280 miles 
per second ; and if the body fell from a great height, the ve- 
locity would be over 350 miles per second: The meteoric 
theory was founded on this law, and is, in substance, that the 
heat of the sun is kept up by the impact of meteors upon his 
surface. The fact that the earth in its course around the sun 
encounters millions of meteoroids every day is shown by the 
frequency of shooting -stars, and leads to the result that the 
solar system is, so to speak, crowded with such bodies revolv- 
ing in all sorts of erratic orbits. It is therefore to be sup- 
posed that great numbers of them fall into the sun ; and the 
question whether the heat thus produced can be equal to that 
radiated by the sun is one to be settled by calculation. It is 



THE SOURCES OF THE SUN'S HEAT. 515 

thus found that, in order to keep up the solar heat, a mass of 
matter equal to our planet would have to fall into the sun ev- 
ery century. 

This quantity of meteoric matter is so far beyond all rea- 
sonable possibility that it requires little consideration to show- 
that the supply of solar heat cannot be thus accounted for. 
(July a minute fraction of all the meteoroids or other bodies 
circulating through space or revolving around the* sun could 
strike that luminary. In order to reach the sun, they would 
have to drop directly to it from space, or be thrown into it 
through some disturbance of their orbits produced by planet- 
ary attraction. If meteors were as thick as this, the earth 
would be so pelted with them that its whole surface would be 
made hot by the force of the impact, and all life would be 
completely destroyed. While, then, the sun may, at some past 
time, have received a large supply of heat in this way. it is 
impossible that the supply could always be kept up. 

The Contraction Theory. — It is now known that there i> 
really no necessity for supposing the sun to receive heat from 
any outward source whatever in order to account for the 
preservation of his temperature through millions of years. 
As his adobe cools off it must contract, and the heat trener- 

CD ' ^ 

ated by this contraction will suffice to make up almost the en- 
tire loss. This theory is not only in accordance with the laws 
of matter, but it admits of accurate mathematical investiira- 
tion. Knowing the annual amount of energy which the sun 
radiates in the form of heat, it is easy, from the mechanical 
equivalent of the heat thus radiated, to find by what amount 
he must contract to make it up. It is thus found that, with 
the present magnitude of the sun, his whole diameter need 
contract but 220 feet a year to produce all the heat which he 
radiates. This amounts, in round numbers, to a mile in 25 
years, or four miles in a century. 

The question whether the temperature of the sun will be 
raised or lowered by contraction depends on whether we sup- 
pose his interior to be gaseous, on the one hand, or solid or 
liquid, on the other. A known principle of the contraction of 



516 



THE STELLAR UNIVERSE. 



gaseous bodies, and one which, at first sight, seems paradox- 
ical, is that the more heat such a body loses, the hotter it will 
become. By losing heat it contracts, but the heat generated 
by the contraction exceeds that which it had to lose in order 
to produce the contraction.* When the mass of gas is so far 
contracted that it begins to solidify or liquefy, this action 
ceases to hold, and further contraction is a cooling process. 
We cannot yet say whether the sun has or has not begun to 
solidify or liquefy in his interior, and therefore cannot make 
an exact estimate of the time his heat will last. A rough 
estimate may, however, be made from the rate of contraction 
necessary to keep up the present supply of heat. This rate 
diminishes as the sun grows smaller at such a rate that in five 
millions of years the sun will be reduced to one-half his pres- 
ent volume. If he has not begun to solidify now, it seems 
likely that he will then, and his heat must soon after begin 
to diminish. On the whole, it is quite improbable that the 
sun can continue the radiation of sufficient heat to support 
life on the earth ten millions of years more. 

The contraction theory enables us to trace the past history 
of the sun a little more definitely than that of his future. He 
must have been larger a hundred years ago than he is now by 
four miles, and yet larger in preceding centuries. Knowing 



* This curious law of cooling masses of gas was discovered by Mr. J. Homer 
Lane, of Washington. This gentleman's paper on the theoretical temperature of 
the sun, in the American Journal of Science for July, 1870, contains the most 
profound discussion of the subject with which I am acquainted. The principle in 
question may be readily shown in the following way. If a globular gaseous mass 
is condensed to one-half its primitive diameter, the central attraction upon any 
part of its mass will be increased fourfold, while the surface upon which this at- 
traction is exercised will be reduced to one-fourth. Hence, the pressure per unit 
of surface will be increased sixteen times, while the density will be increased only 
eight times. Hence, if the elastic and gravitating forces were in equilibrium in 
the primitive condition of the gaseous mass, its temperature must be doubled in 
order that they may still be in equilibrium Avhen the diameter is reduced one-half. 
A similar paradox is found in the theorem of celestial mechanics — that the effect 
of a resisting medium is to accelerate the motion of a planet or comet through 
it. The effect of the resistance is to make the body approach the sun, and the 
velocity generated by the approach exceeds that lost by the resistance. 



THE SOURCES OF THE SUN'S HEAT. 517 

the law of liis contraction, we can determine his diameter at 
any past time, just as in the case of the running cluck the 
height of the weight during preceding days can be calculated. 
We can thus go back to a time when the globe of the bud ex- 
tended out to the orbit of Mercury, then to the orbit of the 
earth, and, finally, when it filled the whole space now occupied 
by the solar system. We are thus led by a backward process 
to the doctrine of the nebular hypothesis in a form strikingly 
similar to that in which it was presented by Kant and La- 
place, although our reasoning is founded on natural law - 
which those great thinkers had no knowledge. 

If we take the doctrine of the sun's contraction as furnish- 
ing the complete explanation of the solar heat during the whole 
period of the sun's existence, we can readily compute the total 
amount of heat which can be generated by his contraction 
from any assigned volume. This amount has a limit, however 
great we may suppose the sun to have been in the beginning: 
a body falling from an infinite distance would generate only 
a limited quantity of heat, just as it would acquire only a lim- 
ited velocity. It is thus found that if the sun had, in the be- 
ginning, filled all space, the amount of heat generated by his 
contraction to his present volume would have been sufficient 
to last 18,000,000 years at his present rate of radiation. We 
can say with entire certainty that the sun cannot have been 
radiating heat at the present rate for more than this period un- 
less he has, in the mean time, received a miraculous accession 
of enerow from some outside source. We use the term " mi- 
raculous" to designate any seeming incompatibility with those 
well -ascertained natural laws which we see in operation 
around us. These laws teach us that no body can acquire 
heat except by changes in its own mass akin to contraction of 
its parts, or by receiving it from some other body hotter than 
itself. The heat evolved by contraction from an infinite size, 
or by the falling of all the parts of the sun from an infinite 
distance, shows the extreme limit of the heat the sun could 
acquire from internal change, and this quantity, as just stated, 
would last only 1S,000,000 years. In order that the sun 



518 THE STELLAR UNIVERSE. 

should receive heat from another body, it is not merely neces- 
sary that that body should be hotter than the sun, but it would 
have to be so much hotter that the small fraction of its radi- 
ant heat which readied the sun would be greater than all that 
the sun himself radiated. To give an instance of what this 
condition requires, we remark that the body must radiate 
more heat than the sun in the proportion that the entire vis- 
ible celestial sphere bears to the apparent angular magnitude 
of the body as seen from the sun. For instance, if its appar- 
ent diameter were twelve degrees, it would seem to fill about 
y oVtf P ai 't °f the celestial sphere, and in order to warm the 
sun at all it would have to radiate more than three thousand 
times as much heat as the sun did. Moreover, in order to fur- 
nish sufficient heat to last the sun any given length of time, 
it would have to stay in the sun's neighborhood so long that 
the excess of what the sun received over what he radiated 
would furnish a supply of heat sufficient for that time. We 
cannot suppose the sun to have received even a supply of a 
thousand years of heat in this way without the most extrava- 
gant assumptions respecting the volume, the temperature, and 
the motion of the body from which the heat was received — 
assumptions which, in addition to their extravagance, would 
involve the complete destruction of the planets by the heat of 
the body, and the total disarrangement of their orbits by its 
attraction, if we suppose them to have been in any way pro- 
tected from this heat. 

The foregoing computation of the limit of time the sun can 
have been radiating heat is founded on the supposition that 
the amount of heat radiated has always been the same. If 
we suppose this amount to have been less formerly than now, 
the period of the sun's existence may have been longer, and 
in the contrary case it may have been shorter. The amount 
in question depends on several causes, the effect of which can- 
not be accurately computed — namely, the magnitude, temper- 
ature, and condition of the solar globe. Supposing a uniform 
radiation, the diameter of this globe was twice as great nine 
millions of years ago as it is now. Its surface was then of 



SECULAR COOLING OF THE EARTH. 519 

four times its present extent, so that, if it was of the same 
nature and at the same temperature as now, there would have 
been four times the radiation. But its density would have 
been only one-eighth as great as at present, and its temper- 
ature would have been lower. These circumstances would 
tend to diminish its radiation, so that it is quite possible that 
the total amount of heat radiated was no greater than at 
present. The probability would seem to be on the side of a 
greater total radiation, and this probability is strengthened by 
geological evidence that the earth was warmer in its earlier 
ages than now. If we reflect that a diminution of the solar 
heat by less than one-fourth its amount would probably make 
our earth so cold that all the water on its surface would 
freeze, while an increase by much more than one-half would 
probably boil the water all away, it must be admitted that the 
balance of causes which would result in the sun radiating heat 
just fast enough to preserve the earth in its present state has 
probably not existed more than 10,000,000 years. This is. 
therefore, near the extreme limit of time that we can suppose 
water to have existed on the earth in the fluid state. 

§ 4. Secular Cooling of the Earth* 

An instance of a progressive loss of heat, second in impor- 
tance only to the loss from the sun itself, and, indeed, con- 
nected with it, is afforded by the secular cooling of the earth. 
As we have shown in a preceding chapter, the interior of the 
earth is hotter than the surface, and wherever there is such 
a difference of temperature as this, there must be a conduc- 
tion of heat from the hotter to the colder parts. In order 
that heat may thus be conducted, there must be a supply of 
heat inside. The increase of heat downwards into the earth 
cannot, therefore, terminate suddenly, but must extend to a 
great depth. 

Whatever view we may take of the question of the earth's 
fluidity, it must be admitted that it was hotter in former a^es 
than now. To borrow an illustration from Sir William Thom- 
son, the case is much the same as if we should find a hot stone 



520 TEE STELLAR UNIVERSE. 

in a field. We could say, with entire certainty, that the stone 
had been in the fire, or some other hot place, within a limited 
period of time. Respecting the origin of this heat, two hy- 
potheses have prevailed — one, founded on the nebular theory, 
that the earth was originally condensed as a molten mass, and 
has not yet cooled off; the other, that it received its heat from 
some external source. The latter was the view of Poisson, 
who accounted for the increase of temperature by supposing 
that the solar system had, at some former period, passed 
through a hotter region of space than that in which it is now 
found. This view is, however, now known to be entirely un- 
tenable, for several reasons. Space itself cannot be warm, 
and the earth could have derived heat only from passing near 
a hot body. A star passing near enough to heat up the earth 
would have totally disarranged the planetary orbits, by its at- 
traction, and destroyed all life on the surface of the globe by 
its heat. 

Thus, tracing back the earth's heat, we are led back to the 
time when it was white-hot ; and then, again, to when it was 
enveloped in the fiery atmosphere of the sun ; and again, when 
it was itself a mass of fiery vapor. Respecting the time re- 
quired for it to cool off, we cannot make any exact calcula- 
tion, as we have done in the case of the sun, because the cir- 
cumstances are entirely different. Owing to the solidity of at 
least the outer crust of the earth, the heat which it loses bears 
no known relation to its interior temperature. In fact, were 
we to compute how long the earth might have been able to 
radiate heat at its present rate, we may find it to be counted 
by hundreds or thousands of millions of years. The kernel 
of the difficulty lies in the fact that when a solid crust once 
formed over the molten earth, there was a sudden change in 
the rate of cooling. As lon^ as the ^lobe was molten, there 
would be constant currents between its surface and the inte- 
rior, the cooling superficial portion constantly sinking down, 
and being replaced by fresh hot matter from the interior. 
But when a continuous solid crust was once formed, the heat 
could reach the surface only by conduction through the crust, 



SECULAR COOLING OF THE EARTH. 521 

and the latter, though only a few feet thick, would operate as 
;i screen to prevent the further loss of heat. There would, as 
the crust cooled, he enormous eruptions of molten matter from 
the interior; but these would rapidly cool, and thus help to 
thicken the crust. 

A fact not to be lost sight of, and which in some way as- 
similates the earth to the sun, is that of the heat lost by the 
earth by far the greater part is made up, not by a lowering 
of the temperature of the earth, but by its contraction. It is 
true that there must be some lowering of temperature, bat for 
each degree that the temperature is lowered there will proba- 
bly be a hundred degrees of heat evolved by the contraction 
of our globe. Considering only the earth, it is difficult to set 
an exact limit to the time it mav have been coolimr since its 
crust was formed. 

The sudden change produced in the radiation of a molten 
body by the formation of a solid crust over its surface may 
afford us some clue to the probable termination of the heat- 
giving powers of the sun. Whenever the latter so far cools 
off that a continuous solid crust is formed over its surface, it 
will rapidly cease to radiate the heat necessary to support life 
on the globe. At its present rate of radiation, the sun will be 
as dense as the earth in about 12,000,000 years; and it is 
<[uite likely to be long before that time that we are to expect 
the permanent formation of such a crust. 

The general cosmical theory which we have been consider- 
ing accounts for the supposed physical constitution of Jupiter, 
which has been described in treating of that planet. On the 
nebular hypothesis, as we have set it forth, the ages of the 
several planets do not greatly differ. The smaller planets 
would, therefore, cool off sooner than the larger ones. It is 
possible that, owing to the great masses of Jupiter and Saturn, 
their rate of cooling has been so slow that no solid crust is yet 
formed over them. In this case they would appear self-lumi- 
nous, were they not surrounded by immense atmospheres, filled 
with clouds and vapors, which shut off a great part of the 
internal heat, and thus delay the cooling process. 



522 THE STELLAB UNIVERSE. 

§ 5. General Conclusions respecting the Nebular Hypothesis. 

It would seem from what has been said that the widest in- 
ductions of modern science agree with the speculations of 
thinking minds in past ages, in presenting the creation of the 
material universe to our view as a process rather than act. 
This process began when the present material universe was a 
mass of fiery vapor, filling the stellar spaces ; it is still going 
on in its inevitable course, and it will end when sun and stars 
are reduced to dark and cold masses of dead matter. The 
thinking reader will, at this stage of the inquiry, very natu- 
rally inquire whether this view of the cosmogony is to be 
received as an established scientific fact, or only as a result 
which science makes more or less probable, but of the validity 
of which opinions may reasonably differ. We consider that 
the latter is the more correct view. All scientific conclusions 
necessarily rest on the postulate that the laws of nature are 
absolutely unchangeable, and that their operations have never 
been interfered with by the action of any supernatural cause ; 
that is, by any cause not now in operation in nature, or op- 
erating in any way different from that in which it has always 
done. The question of the correctness of this postulate is one 
of philosophy and common-sense rather than of science ; and 
all we can say in its favor is that, as a general rule, the bet- 
ter men understand it, the more difficulty they find in doubting 
it. And all we can say in favor of the nebular hypothesis 
amounts to this: that the operations of nature, in their widest 
range, when we trace them back, seem to lead us to it, as 
the mode of running of the clock leads to the conclusion that 
it was once wound up. 

Helmholtz, Thomson, and others have, as we have explain- 
ed, made it evident that by tracing back the cooling processes 
we now see going forward in nature, we are led to a time 
when the planets were enveloped in the fiery atmosphere of 
the sun, and were therefore themselves in a molten or vapor- 
ous form. But the reverse problem, to show that a nebulous 
mass would or might condense into a system possessing the 



CONCLUSIONS RESPECTING THE NEB LEAR HYPOTHESIS. 523 

wonderful symmetry of our solar system — the planets revolv- 
ing round the sun, and the satellites round their primaries 
in nearly circular orbits — has not been solved in a manner at 
all satisfactory. We have seen that Kant's ideas were in some 
respects at variance with the laws of mechanics which have 
since been discovered. Laplace's explanation of how the 
planets might have been formed from the atmosphere of the 
sun is not mathematical enough to be conclusive. In the ab- 
sence of a mathematical investigation of the subject, it seems 
more likely that the solar atmosphere would, under the condi- 
tions supposed by Laplace, condense into a swarm of small 
bodies like the asteroids, tilling the whole space now occupied 
by the planets. Again, when we examine the actual nebulae, 
we find very few of them to present that symmetry of outline 
which would lead to their condensation into a system so sym- 
metrical as that to which our planet belongs. The double 
stars, revolving in orbits of every degree of eccentricity, and 
the rings of Saturn, composed apparently of a swarm of small 
particles, offer better examples of what we should expect from 
the nebular hypothesis than do the planets and satellites of our 
system. 

These difficulties may not be insurmountable. The greatest 
of them, perhaps, is to show how a ring of vapor surrounding 
the sun could condense into a single planet encircled by satel- 
lites. The conditions under which such a result is possible 
require to be investigated mathematically. At the present, 
time we can only say that the nebular hypothesis is indicated 
by the general tendencies of the laws of nature; that it has 
not been proved to be inconsistent with any fact; that it is 
almost a necessary consequence of the only theory by which 
we can account for the origin and conservation of the sun's 
heat ; but that it rests on the assumption that this conservation 
is to be explained by the laws of nature, as we now see them 
in operation. Should any one be sceptical as to the sufficiency 
of these laws to account for the present state of things, science 
can furnish no evidence strong enough to overthrow his doubts 
until the sun shall be found growing smaller by actual meas- 



524 THE STELLAR UNIVERSE. 

urement, or the nebulae be actually seen to condense into stars 
and systems. 

§ 6. The Plurality of Worlds. 

When we contemplate the planets as worlds like our own, 
and the stars as suns, each, perhaps, with its retinue of attend- 
ant planets, the idea naturally suggests itself that other planets 
as well as this may be the abode of intelligent beings. The 
question whether other planets are, as a general rule, thus 
peopled, is one of the highest interest to us, not only as in- 
volving our place in creation, but as showing us what is really 
greatest in the universe. Many thinking people regard the 
discovery of evidences of life in other worlds as the great ul- 
timate object of telescope research. It is, therefore, extreme- 
ly disappointing to learn that the attainment of any direct 
evidence of such life seems entirely hopeless — so hopeless, 
indeed, that it has almost ceased to occupy the attention of 
astronomers. The spirit of modern science is wholly adverse 
to speculation on questions for the solution of which no scien- 
tific evidence is attainable, and the common answer of astron- 
omers to all questions respecting life in other worlds would 
be that they knew no more on the subject than any one else, 
and, having no data to reason from, had not even an opinion 
to express. Still, in spite of this, many minds will speculate ; 
and although science cannot answer the great question for us, 
she may yet guide and limit our speculations. It may, there- 
fore, not be unprofitable to show within what limits specula- 
tion may not be discordant with the generalizations of science. 

First, we see moving round our sun eight large planets, on 
one of which we live. Our telescopes show us other suns, in 
such numbers that they defy count, amounting certainly to 
many millions. Are these suns, like our own, centres of plan- 
etary systems? If our telescopes could be made powerful 
enough to show such planets at distances so immense as those 
of the fixed stars, the question would at once be settled ; but 
all the planets of our system would disappear entirely from 
the reach of the most powerful telescopes we can ever hope to 



THE PLURALITY OF WORLDS. 525 

make at a distance far less than that which separates us from 
the nearest fixed star. Observation can, therefore, afford 08 
no information on the subject. We must have recourse t<> 
cosmological considerations, and these may lead to the con- 
clusion that if the whole universe condensed from a nebulous 
mass, the same cause which led our sun to be surrounded by 
planets would operate in the case of other suns. But we have 
just shown that the symmetry of form and arrangement seen 
in our system is something we could rarely expect to result 
from the condensation of masses so irregular as those which 
make up the large majority of the nebula 1 , while the irreg- 
ular orbits of the double stars show us what we should rather 
expect to be the rule. It is, therefore, quite possible that reti- 
nues of planets revolving in circular orbits may be rare excep- 
tions, rather than the rule, among the stars. 

Next, granting the existence of planets without number, 
what indications can we have of their habitability ? There 
is one planet besides our own for which the telescope settle- 
this point — namely, the moon. This body has neither air n<»r 
water, and, consequently, nothing on which organic life can 
be supported. The speculations sometimes indulged in re- 
specting the possible habitability of the other side of the 
moon, which we can never see, are nothing more than plays 
of the imagination. The primary planets are all too distant 
to enable us to form any certain judgment of the nature of 
their surfaces, and the little we can see indicates that their 
constitution is extremely varied. Mars has every appearance 
of being like our earth in many particulars, and is, therefore, 
the planet which we should most expect to find inhabited. 
Most of the other planets give indications of being surround- 
ed by immense atmospheres, filled with clouds and vapors, 
through which sight cannot penetrate, and we can reach no 
certain knowledge of what may be under these clouds. On 
the whole, we may consider the chances to be decidedly 
against the idea that any considerable fraction of the heav- 
enly bodies are fitted to be the abode of such animals as we 
have on the earth, and that the number of them which have 



526 THE STELLAR UNIVERSE. 

the requisites for supporting civilization is a very small frac- 
tion indeed of the whole. 

This conclusion rests on the assumption that the conditions 
of life are the same in other worlds as in our own. This as- 
sumption may be contested, on the ground that we can set no 
limits to the power of the Creator in adapting life to the con- 
ditions which surround it, and that the immense range of adap- 
tation on our globe — some animals living where others are im- 
mediately destroyed — makes all inferences founded on the im- 
possibility of our earthly animals living in the planets entirely 
inconclusive. The only scientific way of meeting this argu- 
ment is to see whether, on our earth, there are* any limits to 
the adaptability in question. A cursory examination shows 
that while there are no well-defined limits to what may be 
considered as life, the higher forms of animal life are very 
far from existing equally under all conditions, and the high- 
er the form, the more restricted the conditions. We know 
that no animal giving evidence of self-consciousness is devel- 
oped except under the joint influence of air and water, and 
between certain narrow limits of temperature; that only forms 
of life which are intellectually very low are developed in the 
ocean ; that there is no adapting power exercised by nature on 
our globe "whereby man can maintain a high degree of intel- 
lectual or bodily vigor in the polar regions ; that the heats of 
the torrid zone also impose restrictions upon the development 
of our race. The conclusion which we may draw from this 
is that, if great changes should occur on the surface of our 
globe, if it should be cooled down to the temperature of the 
poles, or heated up to that of the equator, or gradually be cov- 
ered with water, or deprived of its atmosphere, the higher pres- 
ent forms of animal life would refuse to adapt themselves to 
the new state of things, and no new forms of life of equal ele- 
vation would take the place of those destroyed by the change. 
There is not the slightest reason for believing that anything 
more intelligent than a fish would ever live under water, or 
anything more intellectual than the Esquimaux ever be sup- 
ported in regions as cold as the poles. If we apply this con- 



THE PLURALITY OF WOULD- 527 

sideration to the question which now occupies as, we are led 
to the conclusion that, in view of the immense diversity 

conditions which probably prevails in the universe, it would 
he only in a few favored spots that we should expect to find 
any very interesting development of life. 

An allied consideration will lead us to nearly the same con- 
clusion. Enthusiastic writers not only sometime> people the 
planets with inhabitants, but calculate the possible population 
by the number of square miles of surface, and throw in a lib- 
eral supply of astronomers who scan our earth with powerful 
telescopes. The possibility of this it would be presumption 
to deny; but that it is extremely improbable, at least in the 
case of any one planet, may be seen by reflecting on the brev- 
ity of civilization on our globe, when compared with the exist- 
ence of the globe itself as a planet. The latter ha- probably 
been revolving in its orbit ten millions of years; man lias 
probably existed on it less than ten thousand year-; <i\ iliza- 
tion less than four thousand; telescopes little more than two 
hundred. Had an angel visited it at intervals of ten thousand 
years to seek for thinking beings, he would have been disap- 
pointed a thousand times or more. Reasoning from anal 
we are led to believe that the same disappointments might 
await him who should now travel from planet to planet, and 
from system to system, on a similar search, until he had exam- 
ined many thousand planets. 

It seems, therefore, so far as we can reason from analogy, 
that the probabilities are in favor of only a very small frac- 
tion of the planets being peopled with intelligent beings. 
But when we reflect that the possible number of the planets 
is counted by hundreds of millions, this small fraction may 
be really a very large number, and among this number many 
may be peopled by beings much higher than ourselves in the 
intellectual scale. Here we may give free rein to our imagi- 
nation, with the moral certainty that science will supply noth- 
ing tending either to prove or to disprove any of its fancies. 



35 



APPENDIX 



i. 

LIST OF THE PRINCIPAL GREAT TELESCOPES OF TIIE WORLD. 
A. Reflecting Telescopes. 



Owner, and Place. 



Construction.* 


Aperture. 


Newtonian. 


6 feet. 


NCw tonian. 


4 feet. 


Cassegr. 


4 feet. 


Newt, S. G. 


47 in. 


Newtonian. 


3 feet 


Cass., S. G. 


28 in. 


S. G. 


31.5 in. 


S.G. 


31.5 in. 


Newtonian. 


2 feet. 



When built, and by whom. 



The Earl of Rosse, Parsonstown, 
Ireland 

Mr. Lassell, Maidenhead, Eng- 
land 

The Observatory of Melbourne, 
Australia 

The Observatory of Paris 

The Earl of Rosse, Parsonstown, 
Ireland 

Professor Henry Draper, Dobbs 
Ferry, New York 

The Observatory of Toulouse, 
France 

The Observatory of Marseilles, 
France 

Mr. Lassell, Maidenhead, Eng- 
land 



Earl of R., 1844. 
Mr. Lassell, f I860. 

Mr. Grubb, U 

\ If. Martin and If. 

( Eiehens, 1875. 

The owner. 
The own.r. 

If. Foucault. 

\ ML Foucault and M. 
1 Eiehens. 

The owner. 



I } . Rej raciing Tt U *< ■<>]>< s . 



Owner, and Place. 


Aperture. 


Maker, and Date. 


U . S. Naval Observatory, Washington 

The Imperial Observatory, Vienna! 


26 in. 
26 in. 
25 in. 
19 in. 
18.5 in. 
18 in. 
15 in. 


\ A. Clark and Sons, 

{ 1873. 

Mr. Grubb, 1877. 

( T. Cooke and Sons, 

} 1870. 

Merz and Mahler. 

( A. Clark and Sons, 

( 1862. 

Mr. Fitz, of N. Y. 

f Merz and Mahler, 

} 1843. 




The Observatory of Strasburg, Germany:}; 


Mr. Van der Zee, Buffalo, New York 


The Observatory of Harvard College, Cam- ) 
bridge, Mass ) 



* In this column, "Cassegr." signifies the Cassegraniau construction, described on page 
124. S. G. signifies that the mirror is of silvered glass, 
t Mr. Lassell's four-foot telescope is, the writer believes, dismantled. 
t These telescopes are still unfinished. 



530 



APPENDIX. 



Owner, and Place. 



The Royal Observatory, Pulkowa, Russia 

Mr. William Huggins, London, England* . . . 

Lord Lindsay, Aberdeen, Scotland 

The Observatory of Lisbon, Portugal 

The Observatory, Markree Castle, England . . 

Hamilton College, Clinton, New York 

The Paris Observatoryf 

The Allegheny Observatory, Pennsylvania . . 

Mr. L. M. Rutherf urd, New York 

The Dudley Observatory, Albany, New York. 

The Royal Observatory, Greenwich, Eh£ 
landl. 

Michigan University, Ann Arbor , 

Vassar College, Poughkeepsie, New York , 

The Physical Observatory, Oxford, England 

The Imperial Observatory, Vienna , 

The Cambridge Observatory, England 

The Royal Observatory, Dublin 

Professor Henry Draper, Dobbs Ferrv, New ) 
York.. f 

The Pritchett Institute, Glasgow, Missouri , 

Mr. S. V. White, Brooklyn, New York 

The Radcliffe Observatory, Oxford, England 

The Observatory, Bothkamp, Germany 

The Observatory, Cordova, South America 

The Observatory, Munich, Germany 

The Observatory, Copenhagen, Denmark 

The Observatory of Cincinnati, Ohio 

Middletown University, Connecticut , 



Aperture. 



15 in. 

15 in. 
15 in. 
14.8 in. 
14 in. 
13.5 in. 
13 in. 
13 in. 
13 in. 
13 in. 



12.5 in. 

12.5 in. 

12.3 in. 

12.2 in. 

12 in. 

12 in. 
12 in. 

12 in. 

12 in. 

12 in. 
12 in. 
11.7 in. 
11.2 in. 
11 in. 
11 in. 
11 in. 
11 in. 



Maker, and Date. 



Merz and Mahler, 
1840. 
Mr. Grubb. 
Mr. Grubb. 
Merz and Mahler. 



Mr. Spencer. 
M. Eichens. 



The owner. 

Mr. Fitz, of N. Y. 

f Merz and Sons, 

J 1860. 

] Troughton and 

(_ Simms. 

Mr. Fitz, of N. Y. 

Mr. Fitz, of N. Y. 

A. Clark and Sons. 
Mr. Grubb. 

A. Clark and Sons, 
1876. 
M. Cauehoix. 
M. Cauehoix. 
\ A. Clark and Sons, 
( 1876. 

A. Clark and Sons, 
1876. 
A. Clark and Sons. 
M. Cauehoix. 
Schroeder. 
Mr. Fitz, of N. Y. 
Merz. 
Merz. 
Merz. 
A. Clark and Sons. 



Besides these, the following telescopes are projected: A reflector of 
seven or eight feet aperture, by Grubb of Dublin, for the Lick Observa- 
tory of California, and a refractor of 28 or 29 inches aperture, by Alvan 
Clark and Sons, for Yale College. 



* This telescope belongs to the Royal Society, but is iu possession of Mr. Huggins. 

t The object-glass is an old one, but the mounting is new, by Eichens. 

t The object-glass is by Merz, of Munich, the mounting by Troughton and Simms. 



LIST OF THE M011E 11EMAUKABLE DOC BEE STABS. 531 



II. 
LIST OF THE MORE REMARKABLE DOUBLE STARS. 

COMPILED BY S. W. Ill T.MIA.M. 



35 Pisciuin . 

38 " . 

42 

51 

55 

// Cassiopeae 
36Andromedae 

(j> Pisciuin . . . 

12 Oeti 

olarie 

>■ Sculptoris. . 
a Piscium . . . 

y Andromeda? 

Trianguli. 
i Cassiopeae 



84 Ceti.. 
y Ceti.. . 

t A riot is. 

£ Persei. 



e Persei . . . 
S9 Eridani. 
Tauri . . . 
a Ononis . . 

•« •• 

23 " . . 



£ Ononis 

1 1 Monocerotis 



12 Lyncis. 



Right Asren. 



8 47 

11 13 
16 13 
26 12 

33 36 

41 43 
Is 32 

1 7 14 
13 ll 
13 45 
40 1 

55 50 

56 32 

2 5 26 
19 10 

35 1 

37 5 
52 21 

3 46 35 

49 48 

4 8 41 

12 58 

5 7 1 
8 46 

16 32 
18 27 

28 32 

29 23 
32 43 

34 42 

6 23 

35 38 



Declination 

1880. 



8 9 
8 12 

12 49 
6 18 

20 17 

:.T 1 1 

22 59 

23 57 
-1 s 

88 W 

25 39 

2 11 

41 45 

29 46 
66 52 



-1 12 

2 I I 

20 52 

:;i 32 

39 40 

-10 33 



5 28 
2 40 



2 

6 5 



>9 34 



F'ositi'n 
Angle. 



149.8 

237.6 

338.0 

82.3 

192.7 

140.0 
368.9 
22 7.:. 
351.4 
210.1 
69.6 
322.2 

62.4 

80.6 
265.] 
L07.3 
824.7 
289.2 
201.9 



207.6 

9.2 
153.7 

245.5 
63.4 

198.8 
28.1 
83.8 
40.3 



236.:. 

84.5 

151.3 

130.0 

101.7 

153.7 
304. 2 



L1.63 



4 
29, 

27 

6 

5 
1 
7 
1 

18.27 
5.53 
3.12 

10.33 



12.47 



Magnitudes. 






5.0 

6.4 

7.1 



8.1 



2.7 9.3 



4.1 



10. 
.5 

5. 

5. 
.0 

6. 
.4 



\ White, 2. Pale-white: 
\ violet, Smyth. 



\ Yellow : blue -green, 

l HerecheL 
White : ashy. 

I Yellow : deep - red, 

/ Dembowski. 
I'llow : purple. 
Binary, 3 19.1 yi 

White : blue. 



White : dull red. 

< Yellow : blue. B 
gain double, .6. 

Yellow : blue. 
A and B. I 
A and C. \ 
Yellow : ashy. 
Yellow : blue. 
Binary. 

^ Light -green : ashy. 
Other small 

f in the held. 
Pale-white : lilac. 
Fellow : bhlr. 
Red : bluish. 
Yellow : blue. 



Discovered by Dawes. 

Yellow : purple. 
\ Sextuple. In the great 
'( nebula of Orion. 

A and B. { 

A and C. J 

Yellow : light-purple. 

A and B. 

B and C. 

A and B. 

A and C. 



532 



APPENDIX. 






Right Ascen. 
1880. 


Declination 
1880. 


Positi'n 
Angle. 


Distance. 


Magnitudes. 


H. M. S. 


o ' 





» 




38 5 


43 42 


17.1 


55.38 


6.0 9.0 


50 36 


-13 53 


343.5 


3.22 


4.7 8.0 


7 12 57 


22 12 


196.9 


7.14 


3.2 8.2 


26 57 


32 9 


239.3 


5.49 


2.7 3.7 


42 19 


-11 54 


17.5 


3.32 


5.3 7.4 


8 5 19 


18 1 


130.1 


0.74 


5.0 5.7 






132.0 


5.48 


5.5 


b il 23 


37 19 


240.2 


2.69 


4.0 6.7 


10 13 20 


20 27 


111.2 


3.18 


2.0 3.5 


37 7 


5 23 


240.5 


6.72 


6.1 7.2 


11 11 48 


32 13 


317.6 


1.09 


4.0 4.9 


48 51 


47 9 


36.4 


3.71 


6.0 8.3 


58 8 


22 8 


240.6 


3.73 


6.0 7.5 


12 29 6 


19 2 


271.9 


20.42 


4.7 6.2 


35 36 


-0 47 


159.3 


4.77 


3.0 3.0 


47 23 


21 54 


25.3 


1.43 


5.0 7.8 






124.7 


28.60 


9.0 


13 37 2 


4 9 


235.3 


3.39 


5.8 8.2 


14 35 25 


14 15 


303.2 


1.02 


3.5 3.9 


39 45 


27 35 


320.6 


2.63 


3.0 6.3 


45 51 


19 36 


301.6 


.5.44 


4.7 6.6 


59 51 


48 7 


239.8 


4.80 


5.2 6.1 


15 19 58 


37 48 


171.9 


108.46 


4.0 






141.9 


0.69 


6.7 7.3 


29 5 


10 56 


196.9 


2.56 


3.0 4.0 


57 46 


-11 3 


173.1 


1.06 


4.9 5.2 






70.3 


7.05 


7.2 


16 22 2 


-26 10 


268.7 


3.46 


1.0 7.0 


17 7 59 


-26 25 


227.3 


5.55 


6.0 6.0 


9 10 


14 32 


118.5 


4.65 


3.0 6.1 


19 33 


37 15 


307.2 


3.60 


4.0 5.1 


59 23 


2 33 


83.7 


3.48 


4.1 6.1 


18 40 22 


39 33 


26.0 


3.03 


4.6 6.3 


40 24 


39 29 


155.2 


2.57 


4.9 5.2 


40 38 


37 29 


149.7 


43.71 


4.2 5.5 


19 25 53 


27 42 


55.7 


34.29 


3.0 5.3 


43 39 


18 51 


312.8 


8.49 


5.7 8.8 


48 34 


69 58 


354.5 


2.79 


4.0 7.6 


20 4 39 


20 33 


326.7 


11.40 


6.0 8.3 


36 11 


31 53 


49.4 


2.74 


6.0 8.1 


53 5 


3 50 


283.9 


0.06 


5.2 6.2 






76.2 


10.83 


7.1 


57 44 


-6 18 


189.6 


2.66 


5.6 7.7 


21 1 14 


38 8 


115.6 


19.55 


5.3 5.9 


27 6 


70 2 


250.0 


13.57 


3.0 8.0 


22 7 40 


-21 40 


119.4 


4.08 


6.0 8.5 


20 3 


-17 21 


304.5 


8.20 


6.0 6.3 


22 39 


-0 38 


334.5 


3.40 


4.0 4.1 


23 9 35 


-9 44 


312.2 


49.63 


4.5 8.5 


52 56 


55 5 


323.4 


3.01 


5.4 7.5 



56 Aurigae.. . 
/x Canis Maj. . 
d Geminorum 

Castor 

5 Navis 

£ Cancri 



38 Lyncis. . . . 
y Leonis 
35 Sextantis . 
| Ursae Maj. . 
65 Ursae Maj. 

g Comae 

24 " 

y Virginis . . . 
35 Comae 



84 Virginis 
Z, Bootis.. . 

€ " ... 

I " ... 

44 " ... 
/z « ... 



8 Serpentis . 
£ Librae .... 



Antares .... 
36 Ophiuchi 
a Herculis . . 

P " ... 

70 Ophiuchi 
e 1 Lvrae .... 
e 2 " .... 

r " 



/3 Cygni . . . 
£ Sagittae . . 
e Draconis 
9 Sagittae . . 
49 Cygni . . 
e Equulei . . 



12 Aquarii. 
61 Cygni . . 
/3 Cephei . . 
41 Aquarii. 
53 " . 
I " . 

ip " 



White: blue. 



A and B. 

A and C. 



Yellow : greenish. 
Yellow: blue. 
Binary. 
Yellow : blue. 



Binary. 
A and B. ) 
A and C. ) 
Yellow : blue. 



Yellow : blue or green. 

Yellow : reddish purple, 

Yellowish : bluish. 

A and B. ) Binary 

B and C. f 

Binary. 

A and B. ) Binary. 

A and C. f 

Red : green. 

Yellow : emerald. 

Yellow : purple. Binary 



Golden yellow : blue. 
Light-green: blue. 
Yellow : blue. 

Yellow: blue. 
A and B. 
A, B\ and C. 
Yellowish : blue. 

Light-green: blue. 
Yellow : blue. 
White : yellow. 
Binary. 
Yellow: blue. 
White: blue. 



Note.— The sign minus (— ) before declinations means south; without the sigu, it is 
north. 



LIST OF NEBULA AXb STAR CLUSTERS. 



533 



III. 



LIST OF THE MORE INTERESTING AND REMARKABLE NEBULA AND 
STAR CLUSTERS. 



Object. 



47 Toucani cluster 

Great nebula of Andromeda 
Nebula 



Tempel'a variable nebula. 

Hind's variable nebula.. . 
Globular cluster 



Great nebula of Orion 

Chacornac's variable nebula. 

Nebula around s Ononis. 

Looped nebula 

Cluster and nebula MeSB 16 

Star cluster 

Mess. 67 

Planetary nebula 



Nebula 

Planetary nebula 



Spiral nebula ' . 

u (i 

Nebula 



Star cluster 

Bifid nebula 

Cluster around u Centauri 

Spiral or ring nebula 

Spiral nebula 



Cluster. 



R. A . ■•- 


Dec. 1*80. 


H. M. 


O ' 


u 19 


72 i - 




10 i ■: N 


12 


25 : 


:; 29 






- \ 


l 16 


19 U N. 


5 9 


68 55 S. 


5 10 


4<» 11 S. 


5 89 


5 - 




21 - \ 


5 SO 


1 17 S. 




69 10 S 


7 36 


14 : 


: 18 


38 1 - 


- 15 


12 15 N. 


9 11 


36 7 - 


9 18 


:,7 17 - 


9 15 


- V 


10 2 


39 51 S. 


10 19 


18 


11 8 


55 10 N. 


12 13 


16 :» N. 


12 17 


16 2 


12 34 


10 :.7 s. 


12 36 


33 12 N. 


13 7 


18 4^ V 


13 18 


42 23 S. 


13 20 


46 41 S. 


13 25 


4 7 49 N. 


13 30 


•29 1( S 


13 32 


17 16 S. 


13 37 


28 59 N. 



534 



APPENDIX. 



Object. 


R. A. 1880. 


Dec. 1880. 


Cluster 


H. M. 

15 12 

15 38 

16 10 
16 37 
16 41 
16 51 
16 52 

16 54 

17 14 
17 22 
17 31 
17 55 

17 57 

18 14 
18 29 

18 49 

19 5 

19 54 

20 11 
20 17 
20 40 

20 58 

21 27 
21 34 
23 20 


O ' 

2 33 N. 

37 23 S. 

22 41 S. 
36 42 N. 

1 44 S. 

3 54 S. 
44 29 S. 

29 56 S. 

38 21 S. 

23 39 S. 
3 10 S. 

23 2 S. 

24 21 S. 
16 13 S. 
24 OS. 
32 53 N. 

50 N. 

22 24 N. 

30 12 N. 
19 44 N. 
30 17 N 
11 50 S. 

1 22 S. 

23 43 S. 
41 53 N. 


(( 


Resolvable nebula 


Great Cluster of Hercules 


Cluster 


a 


a 


u 


Small annular nebula 

M (( (( 


Cluster 


Trifid nebula 


Nebulous cluster 


Hooked nebula 


Cluster 


Annular nebula of Lyra 

Variable nebula 


Dumb-bell nebula 


Small annular nebula 


Planetary nebula 


Nebula around k Cygni 

Planetary nebula 

Cluster 


u 


Blue planetary nebula 



To facilitate the finding of the above nebulae and clusters, their posi- 
tions are marked on the star-maps with small circles. 



J'EL'IODIC COMETS SEES AT MORE THAN ONE RETURN. 535 



= H 









= z X 






O I- • - 
— ' — i z 



- - 



-: C S? 



-- 


■M 


— ' 


--' 


l~ 


.-' 


_" 


--' 


.-' 


t- 


• ~ 


t- 


I- 




I- 


t- 


fc- 




X 


X 


X 


X 


X 


QO 


X 


X 


>: 



8 5 
pq p 



- ~ r 



536 



APPENDIX. 



> 





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538 



APPENDIX. 



VI. 



ELEMENTS OF THE SMALL PLANETS. 

COMPILED BY D. P. TODD. 



Sign and Name. 



(1) Ceres 

(2) Pallas 

(3) Juno 

(4) Vesta 

(5) Astraea 

(6) Hebe 

(7) Iris 

(8) Flora 

(9) Metis 

(lO)Hygeia 

(11) Parthenope 

(12) Victoria.... 

(13) Egeria 

(14) Irene 

(15) Eunomia... 

(16) Psyche 

(17) Thetis 

(18) Melpomene, 

(19) Portuna. . . . 

(20) Massalia . . . 

(21) Lutetia 

(22) Calliope.... 

(23) Thalia 

(24) Themis 

(25) Phocaea 

(26) Proserpine . 

(27) Euterpe.... 

(28) Bell on a.... 

(29) Amphitrite. 

(30) Urania 



£ .2 



1801 
1S02 
1804 
1807 
1845 

1847 
1847 
1847 
184S 
1849 

1850 
1850 
1S50 
1851 
1851 

1852 
1852 
1852 
1852 
1852 

1852 
1852 
1852 
1853 
1853 

1S53 
1S53 
1854 
1854 
1854 



Piazzi 

Olbers 

Harding.... 

Olbers 

Heucke 

Hencke 

Hind 

Hind 

Graham 

Gasparis — 

Gasparis — 

Hind 

Gasparis — 

Hind 

Gasparis — 

Gasparis. . . . 

Luther 

Hind 

Hind 

Gasparis. 

Goldschmidt 

Hind 

Hind 

Gasparis 

Chacornac. 

Luther 

Hind 

Luther 

Marth 

Hind 



2.98 
3.43 
3.35 

2.57 
3.06 

2.92 
2.94 

2.55 
2.68 
3.49 

2.70 
2.84 
2.80 
3.01 
3.14 

3.33 
2.79 

2.80 
2.83 
2.75 

2.83 
3.20 
3.24 
3.52 
3.01 

2.89 
2.76 
3.20 
2.71 
2.66 



as 

ft 



2.56 
2.11 
1.9.8 
2.15 
2.10 

1.93 
1.83 
1.86 
2.09 
2.80 

2.21 
1.82 
2.35 
2.17 
2.15 

2.52 
2.15 
1.80 
2.05 
2.06 

2.04 
2.62 
2.02 
2.75 
1.79 

2.42 
1.94 
2.35 
2.34 

2.06 



£> g 

ft I 



770.2 
768.9 
814.1 
977.8 
856.9 

939.9 
962.6 
1086.3 
962.3 
636.4 

924.0 
994.8 
857.9 
851.0 
825.4 

710.8 
912.4 
1020.1 
930.1 
948.9 

933.6 
715.2 
832.4 
639.0 
954.2 

819.7 
986.7 
766.6 
S69.0 
975.4 



.1 I 



Yrs. 
4.61 
4.62 
4.36 
3.63 
4.14 

3.78 
3.69 
3.27 
3.69 
5.5S 

3.84 
3.57 
4.14 
4.17 
4.30 

4.99 
3.89 
3.48 
3.82 
3.74 

3.S0 
4.96 
4.27 
5.56 
3.72 

4.33 
3.60 
4.63 
4.09 
3.64 



0.077 
0.238 
0.257 
0.089 
0.186 

0.203 
0.231 
0.156 
0.123 
0,109 

0.100 
0.219 

0.087 
0.163 
0.187 

0.139 
0.129 
0.218 
0.159 
0.143 

0.162 
0.101 
0.231 
0.124 
0.255 

0.0S7 
0.174 
0.153 
0.074 
0.127 



150.0 
122.0 
54.9 
250.9 
134.9 

15.2 
41.4 
32.9 

71.1 
238.3 

317.9 
301.7 
120.2 
ISO. 3 
27.9 

15.1 
261.3 
15.1 
31.1 
99.1 

327.1 
59.9 

123.8 
144.1 
302.8 

236.4 
88.0 

122.4 
56.4 
32.1 



3° 



80.8 
172.8 
170.9 
103.5 
141.5 

138.7 
259.8 
110.3 
6S.5 

285.5 

125.2 
235.6 
43.2 
86. S 
293.9 

150.6 
125.4 
150.1 
211.5 
206.6 

80.5 
66.6 

67.7 
35.S 
214.2 

45.9 

93.9 

144.7 

356.7 

30S.1 



10.' 

34.7 

13.0 

7.1 

5.; 

14.8 
5.5 
5.9 
5.6 
3.8 



8.4 
16.5 

9.1 
11.7 

3.1 
5.6 

10.5 
1.5 
0.7 

3.1 
13.7 

10.2 

0.8 

21.6 

3.6 
1.6 
9.4 
6.1 
2.1 



a 



2.769 
2.771 
2.668 
2.361 
2.579 

2.424 
2.386 
2.201 
2.387 
3.144 

2.452 
2.334 
2.577 
2.591 
2.644 

2.921 
2.473 
2.296 
2.442 
2.409 

2.435 
2.909 
2.629 
3.136 
2.400 

2.656 
2.347 

2.777 
2.525 
2.365 



ELEMENTS OF THE SMALL PLANETS. 



539 



nd Name. 



(31) Eaphrosyne. 

(32) Pomona 

(33) Polyhymnia. 

(34) Circe 

(35) Leucothea... 

(36) Atalanta 

(37) Fides 

(38) Leda 

(39) Laetitia 

(40) Harmouia.. 



(41) Daphne . 
(49)l8is 

(43) Ariadne . 

(44) Nysa 
(46) Eugenia. 



(40) Hestia... 

(47) Aglaia... 

(48) Doris.. .. 

(49) Pales. . . . 

fid) Virginia. 



(51) Nemausa. . 

(52) Europa — 

(53) Calypso . . . 

(54) Alexandra. 

(55) Pandora. . . 



(66) Melete 

(57) Mnemosyne 
(5S) Concordia. . 

(59) Elpis 

(00) Echo 



(61) Danae 

(68) Erato 
(63) Ausonia.. 

(04) Angelina. 

(05) Cybele . . . 



(00) Maia 

V G7) Asia 

(OS) Leto 

(69) Hesperia . 

(70) Panopaea. 



(71) Niobe 

(72) Feronia . . 

(73) Clytia.... 

(74) Galatea... 

(75) Enrydice . 



1S54 
1S54 
1S54 
1855 
1855 

1656 

1855 
1850 
1S56 
1856 

ia-56 
1S56 
1857 
1861 

1S57 

1S57 
1857 
1857 
1S57 
1887 

1898 
L868 

1S5S 
185S 
1858 

1S57 
1859 

1S60 
1S60 
1S00 

IS60 
1S60 
1861 

ISO! 
1S61 

1861 
1S61 
1S01 
1801 
1S01 

1S61 
1S01 
1*02 
1S02 
1S02 



Ferguson 

Goldschmidt. . 

Chacornac 

Chacornac 

Luther 

Goldschmidt . 

Luther 

Chacornac — 

Chacornac 

Goldschmidt.. 



Goldschmidt. 

POgBOU 

Pogsou 

Goldschmidt. 

Goldschmidt. 



Pogsou 

Luther 

Goldschmidt. 
Goldschmidt. 
Ferguson 



Laurent 

Goldschmidt. 

Luther 

Goldschmidt.. 
Searle 



Goldschmidt. 

Luther 

Luther 

Chacornac 

Ferguson 



Goldschmidt. . 

Foerster 

Gasparis 

Tempel 

Tempel 



Tuttle 

Pogsou . . * . . 

Luther 

Schiaparelli.. 

Goldschmidt. 



Luther.. 
Peters. . 
Tuttle . . 
Tempel. 
Peters.. 



3.85 
2.80 
3.83 

2.97 



3.67 

3.11 
3.16 
3.08 
2.37 

3.51 
2.99 
2,61 
2.T9 
2.94 

2.94 

::.'.'. r . 
3.33 
3.81 
3.41 

3.36 

3.15 
:\.-2:< 
3.16 

8.60 
2.81 
3.03 
2.83 

3.4' 
3.6" 



2.09 
3.02 
3.S0 

3.09 
2.87 
3.30 
3.49 
3.09 



2.45 
2.37 
L89 
2.40 
2.32 

1.92 
2.17 
2.32 
2.46 
2.16 

2.02 
1.89 
1.83 
2.00 
2.50 

2.11 
2.50 
2.S9 
2.36 
1.90 

2.21 
2.70 
2.08 

2.17 
2.37 

1.98 

2.S1 
2.59 
2.40 
1.95 

2.50 
2.59 

2.10 
2.34 
3.05 

2.21 
1.97 
2.26 
2.47 
2.14 



635.3 
852.6 
733.3 

686.0 

T-ii.o 
826.4 

7-2.1 

1039.3 

773.3 
930.9 
10S5.0 
940.5 
791.0 

SS4.0 
725.9 
646.4 
655.3 
S21.6 



Vr-. 

5.59 
4.16 
4.84 
4.41 
5.18 

4.55 

4.30 
4.54 
4.61 
3.42 

4.59 

3.81 
3.27 

3.78 
4.49 

4.02 
1.89 
5.49 
5.42 
4.32 



975.4 3.64 



3.23 2.2S 
2.54 1.99 



2.7S 
3.44 
3.49 



2.55 
2.12 
1.S5 



661 

S36.5 
796.6 

774.0 

348.1 

633.0 
799.0 
794,0 
958.3 

687.5 
640.9 

955.0 

55S.9 

S24.0 
941.5 
705.3 
0S9.9 
S39.6 

775.4 

1040.1 

S15.4 

765.6 

S12.3 



5.45 
4.25 
4.40 
4.59 

4.19 
5.01 
4.44 
4.47 
3.70 

5.16 
5.54 

3.72 
4.39 
6.35 

4.32 
3.77 
4.04 
5.15 
4.23 

4.5S 
3.41 
4.35 
4.64 
4.37 



0.223 
0.083 
0.340 
0.107 
0.824 

0.302 
0.177 

0.154 
o.lll 
0.047 

0.270 
0.226 
o.l 07 
0.161 
0.089 

0.165 
0.130 
0.071 

0.235 
0.2S5 

0.067 
0.109 
0.204 

0.199 

0.142 

0.236 
0.109 

0.042 
0.117 
0.1S4 

0.162 
0.173 
0.124 
0.128 
0.110 

0.165 
0.186 

0.1SS 
0.170 

0.1S3 

0.173 
0.120 

0.042 
0.23S 
0.306 



93.4 
193.4 
342.4 
148.7 
302.4 

42.9 

66.5 

lol.2 

3.2 

0.9 



= — 



9.2 
355.S 

359.4 

8.3 

296.4 

157.4 

93.6 



290.0 17'.'. 2 
318.0 B4.6 



•j7-.o 
112.2 
229.0 

354.2 

70.3 
31.6 
10.1 

176.9 

lo7.1 
93.0 

12.1 

294.6 

54.1 

18.4 

9S.6 

344.1 
3S.5 

270.4 
123.7 
2G0.S 

40.4 
306.4 
345.2 
108.5 
299.S 

221.3 

30S.0 

57.9 

S.O 

335.5 



2<;4.;i 
131.1 

181.6 

4.3 

173.S 

175.9 
129.7 



26.5 
5.5 

1.9 
5.4 

1-.7 
3.1 

10.4 

16.0 
8.6 
3.5 
3.7 
6.6 

2.3 
5.0 
6.5 
3.1 

10.0 
7.4 



S - 
- 



144.o .M 
313.8 11.8 



194.1 
200.2 

161.4 
170.4 
192.1 

334.2 

125.7 

311.3 

S.3 

208,8 

45.0 

187.9 

4S.3 

316.5 

207. S 

7.9 

197.9 

35:>.9 



S.O 
15.2 
5.0 
S.6 
3.6 



3.14> 
2.745 

2.440 

3.119 

2,652 
2.365 
2.680 

3.155 
2.393 





2.987 


2.2 


3.130 






1.3 


2.0-1 


3.5 


3.42> 


3.1 


2.650 


6.0 


2.422 


3.0 


2.781 


8.5 


2.930 


11.6 


2.614 


23.3 


2.750 


54 


2.206 


2.4 


2.635 


4.0 


2.7-0 


5.0 


2.072 



540 



APPENDIX. 



Sign and Name. 



(T6) Freia 

(T7) Frigga 

(78) Diana 

(79) Euryuome.. 

(80) Sappho 

(SI) Terpsichore 
'(32) Alcmene . . . 

(83) Beatrix 

(84) Clio 

(85) Io 

(86) Semele 

(87) Sylvia 

(88) Thisbe 

(89) Julia 

(90) Antiope.... 

(91) ^Egina 

(92) TJndina 

(93) Minerva.... 

(94) Aurora 

(95) Arethusa . . . 

(96) Mg\e 

(97) Clotho 

(98) Ianthe 

(99) Dike 

(lOO)Hekate 

(101) Helen a 

(102) Miriam 

(103) Hera 

(104) Clyraene . . . 

(105) Artemis 

(106)Dione 

(107) Camilla .... 
(10S) Hecuba 

(109) Felicitas . . . 

(110) Lydia 

(111) Ate 

(112) Iphigenia . . 

(113) Amalthea.. 

(114) Cassandra.. 
(115)Thyra 

(116) Sirona 

(117) Lomia 

(118)Peitho 

(119) Althaea 

(120)Lachesis.... 






1SC2 



1S63 
1S64 

1864 
1S64 
1805 
1865 
1865 

1866 
1866 
1866 
1866 



1867 
1867 
1867 
1867 

1868 
1S68 
1868 
1868 

1S6S 



1868 
186S 

1868 
1868 

1S68 
1868 
1869 
1869 
1870 

1870 
1870 
1871 
1871 
1871 

1871 
1871 

1S72 
1872 

1872 



D' Arrest 

Peters .. 

Luther 

Watson 

Pogson 

Tempel 

Luther 

Gasparis 

Luther 

Peters 

Tietjen 

Pogson 

Peters 

Stephan 

Luther 

Stephan 

Peters 

Watson 

Watson 

Luther 

Coggia 

Tempel 

Peters 

Borelly 

Watson 

Watson 

Peters 

Watson 

Watson 

Watson 

Watson 

Pogson 

Luther 

Peters 

Borelly 

Peters 

Peters 

Luther 

Peters 

Watson 

Peters 

Borelly 

Luther 

Watson 

Borelly 



4.00 
3.03 
3.16 
2.92 
2.76 

3.45 
8.3S 
2.64 
2.92 
3.16 

3.76 
3.76 
3.21 
3.01 
3.68 

2.87 
3.51 
3.14 
3.44 



3.36 
3.20 
3.46 
3.60 

2.94 
3.47 
2.92 
3.70 

2.79 

3.73 
4.00 
3.54 
3.50 
2.94 



2.74 
2.58 
3.05 
2.84 

3.16 
3.06 
2.83 
2.79 
3.27 



1.97 
1.84 

2.25 
2.15 
2.22 
1.80 
2.15 

2.46 
3.21 
2.32 
2.09 
2.61 

2.31 

2.86 
2.37 
2.89 
2.63 

2.62 
1.98 
2.1S 
2.13 

2.58 

2.23 
1.86 
2.48 
2.60 
1.96 

2.59 
3.12 

2.8S 
1.89 
2.52 

2.32 
2.12 
2.17 
2.30 
1.92 

2.37 
2.92 
2.05 
2.36 
2.97 



563.7 
812.2 
835.3 
928.9 
1019.8 

736.2 
771.4 
936.7 
976.9 

820.7 

646.3 
546.0 
770.2 
870.8 
636.2 

851.8 
623.7 
776.5 
630.7 
657.7 

666.2 

814.2 
804. S 
75S.7 
652.5 

854.2 
817.0 
799.1 
635.0 
970.1 

631.6 

528.2 
616.4 

802.0 
785.4 

849.9 
934.7 

908. S 
810.6 



770.9 
6S6.0 
931.9 
855.0 
643.5 



Yrs. 
6.30 
4.37 
4.25 
3.S2 
3.4S 

4.82 
4.60 
3.79 
3.63 
4.33 

5.49 
6.50 
4.61 

4.08 
5.58 

4.17 
5.69 
4.57 
5.63 
5.40 

5.33 
4.36 
4.41 
4.68 
5.44 

4.16 
4.35 
4.44 
5.59 
3.66 

5.62 
6.72 
5.76 
4.43 
4.52 

4.18 
#.80 
3.66 
4.38 
3.67 

4.60 
5. IS 
3.81 
4.15 
5.52 



0.174 
0.134 
0.205 
0.194 
0.200 

0.211 
0.221 
0.086 
0.236 
0.191 

0.210 
0.079 
0.160 
0.180 
0.169 

0.108 
0.102 
0.140 
0.086 
0.144 

0.140 
0.258 
0.189 
0.238 
0.164 

0.138 
0.303 
0.080 
0.174 
0.175 

0.181 
0.123 
0.103 
0.300 
0.077 

0.105 
0.12S 
0.087 
0.140 
0.194 

0.143 
0.023 
0.161 
0.083 
0.047 



92. 8 
60.4 

121.3 
44.4 

355.3 

48.7 
132.4 
191.8 
339.3 
322.6 

29.7 

335.4 
309.3 
353.4 
301.1 

80.3 
330.8 
274.7 
46.0 
31.2 

163.2 
65.6 

147.6 
240.6 
307.7 

327.4 
354.6 
321.0 
5S.2 
242.8 

27.0 
112.8 
173.5 

56.0 
336. S 

108.7 
338.2 
198.7 
153.1 
43.0 

152.8 
48.8 
77.6 
12.4 

214.0 



3° 



212.2 
2.0 
334.1 
206.7 
218.7 

2.7 
27.0 
27.5 

327.5 



88.1 

76.1 

277.6 

311.7 

71.4 

11.1 

102.9 

5.1 

4.6 

244.3 

322.8 
160.7 
354.4 
41.7 
128.2 

343.7 
212.0 
136.3 
44.0 

18S.0 

63.4 

175.7 

352.4 

4.9 

57.2 

306.2 
324.0 
123.2 
164.4 
309.1 

64.4 
349.6 

47.5 
204.0 



2.0 
2.5 
S.6 
4.6 
8.6 

7.9 
2.9 
5.0 
9.4 
11.9 

4.8 
10.9 

5.2 
16.2 

2.3 



10.2 
5.1 
5.4 
2.9 

21.5 

4.6 

9.8 
4.4 
S.O 
6.0 

4.9 
2.6 
5.0 
4.9 
11.6 

3.6 

15.0 

7.S 
5.S 
7.0 



2.672 
2.623 
2.444 
2.296 

2.853 
2.766 
2.430 
2.363 
2.654 

3.112 
3.482 
2.769 
2.551 
3.145 



2.1 


2.589 


9.9 


3.187 


8.6 


2.754 


8.1 


3.163 


12.9 


3.076 


16.1 


3.050 


11.8 


2.668 


15.6 


2.6S9 


13.9 


2.797 


6.4 


3.092 



2.5S4 
2.662 
2.701 
3.149 
2.374 

3.160 
3.560 j 
3.212 
2.695 i 

2.733 

2.593 i 
2.433 | 
2.376 I 
2.676 | 
2.379 

2.767 
2.991 
2,438 
2.5S0 
3.121 



ELEMENTS OF THE SMALL PLANETS. 



541 



Sign and Nome. 



(121) Hermione. 

(122) Gerda 

(123) Brunhilda. 

(124) Alceste.... 

(125) Liberatrix. 



(120) Velleda. . . 

(127) Johanna . 

(128) Nemesis.. 

(129) Autigone. 

(130) Electra . . . 



(131) Vala 

(132) Mr. bra 

(133) Cyreue 

(134) Soptarosyne 

(135) Hertha 



(130) Austria. . 

(137) Melibcea. 

(138) Tolosa . . 

(139) Juewa... 

(140) Siwa 



(141) Lumen. 

(142) Polana. 

(143) Adrla .. 

(144) Vibilia . 

(145) Adeona 



(14G) Lucina . . 

(147) Protogeneia 

(148) Gallia 

(149) Mednaa 

(150) Nuwa 



(151) Abundantia, 

(152) Atala 

(,153) Hilda 

(154) Bertha 

(155) Scylla 



(150) Xantippe.. 
(157) Dejanira . . 
(15S) Koronis . . . 

(159) Jimilia. . . . 

(160) Una 



(161) Athor . . . 

(162) Lauren tia . . 

(163) Erigone . 

(164) Eva 

(105) Loreley.. 



1872 
1872 
1872 
1872 
L872 

1S72 
1872 
1872 
1873 
1873 

1873 
1873 
1873 
1873 
1S74 

L874 

1S74 
1874 
1874 

1874 

1S75 
1876 

1S75 
1875 
1S75 

L87B 

1875 
1875 
1S75 
1875 

1S75 
1S75 
1875 
1S75 
1876 

1S75 
1S75 
1876 

1S70 
1876 

1876 
1S76 
1S76 
1S76 

1S76 



Watson 

Peters 

Peters 

Peters 

Prosper Henry. 

Paul Henry.. .. 
Prosper Henry. 

Watson 

Peters 

Peters 



Peters. . 

Watson. 
Watson. 

Lather 

Peters.. 



Pallsa... 

Palisa. .. 
Per rot in, 

Watson.. 
Palisa... 



Paul Henry. 

Palisa 

Palisa 

Peters 

Peters 



Borelly 

Schulhof. 

Prosper Henry. 

Perrotin 

Watson 



3.Ss 
3.34 
3.00 
2.84 
4.09 

2.70 
2.92 
3.10 
8.47 

3.77 

2.62 
3.59 
3.48 
2.87 
2.98 

2.4S 
3.78 
2.83 
2.96 



3.03 
3.10 
2.38 
2.42 
1.98 

2.18 

2.59 
2.411 
2.28 
2.47 

2.22 
1.61 
2.04 
2.27 
1.93 



552.5 
614.1 



Yre. 
6.43 
5.78 



903.4 L42 

832.0 4.27 

071.0 5.29 

931.0 3.81 

775.9 4.5s 



777.5 
727.4 
643.9 

942.8 
846.1 
662.2 
664.6 
837.1 



2.09 1025.9 
2.4S 639.7 



2.06 
2.67 

3.32 2.14 



3.31 2.10 



Palisa 

Paul Henry. 

Palisa 

Prosper Henry. 
Palisa 

Palisa 

Borelly 

Kuorre 

Paul Henry. 
Peters 



Watson 

Prosper Henry 

Perrotin 

Paul Henry.. .. 
Peters 



2.64 
2.93 
3.27 
3.27 



3.22 
3.28 

2.39 
3.3S 

2.S4 
3.39 

4. Gi> 
3.54 



3.S4 
3.16 
3.86 

3.49 
2.90 



3.54 
2.71 
3.37 
3.36 



2.14 
2.57 
2.03 
2.12 

2.53 
3.03 

2. -JO 
l.SS 
2.59 

2.33 
2.87 
3.31 
2.90 



2.24 
2.02 
2.12 
2.70 
2.57 

2.00 
2.52 
2.00 
1.73 
2.90 



92S.8 
751.0 
786.9 



4.57 
4.88 
5.51 

3.77 

4.-.'' i 
5.36 
4.12 



0.122 
0.037 
0.115 
0.078 
0.347 

0.106 
0.066 
0.126 
0.807 
0.208 

0.082 

0.3S0 
0.137 
0.117 



C J 



3.79 0.206 



3.46 

5.55 
3.S2 
4.72 
4 52 



795.6 4 16 

962.0 3.69 

777.0 4.57 

822.4 4.32 

502.5 4.42 



796.3 
642.2 
769. S 
1139.2 
685.2 

854.2 
640.1 
451.9 
613.S 



070.2 
S53.4 
686.2 

642.2 
783.0 

96S.S 
673.1 

9S2.1 
870. 1 
641.2 



4.40 
5.53 
4.61 
3.12 
5.18 

4.10 
5.55 

7.80 
5.78 



5.30 
4.16 
5.17 
5.53 
4.53 

3.66 

5.28 
3.62 
4. OS 
5.54 



0.085 
0.908 
0.158 
0.051 

0.216 

0.223 
0.105 
0.066 
0.233 
0.218 

0.067 
0.030 
0.185 
0.119 
0.132 

0.100 
0.082 
0.163 

0.100 



0.264 
0.220 
0.292 
0.116 
0.061 

0.133 
0.169 
0.149 
0.321 
0.073 



1.3 

208.9 

T2.9 

245.7 
251.3 

34T.8 

122.6 

16.6 

241.0 

20.5 

258.6 
152.4 
248.3 
66.9 

319.8 

316.5 
310.3 
311.4 
115.5 
300.6 

22.6 
227.4 
223.3 
8.3 
118.1 

237.7 
84.7 
36.0 

357.5 

215.9 
SO.O 
2S5.0 

168.7 

155.9 
109.2 
355.2 

100.7 
56.S 

312.9 

143.0 

93.3 

2.S 



77.0 
179.0 
30$. 5 
188.4 
171.3 

23.1 
31.8 
70.5 
138.0 
146.0 

65.3 
260.0 
321.2 
346.5 
344.0 

186,2 

204.3 
54.9 
358.6 
107.0 



7.6 
1.0 
6.5 
2.9 
6.1 

2.9 

8.3 
6.3 

12.2 
22.9 

4.6 
25.0 

7.2 
11.6 

2.3 

9.6 

13.8 
3.2 

3.2 



319.1 11.5 
292.6 2.3 



333. S 
76.8 
77.7 

S4.4 
252.5 
145.1 
160.1 
207.5 

40.(1 

41.5 

22S.3 

37.6 



02.4 
282.8 
135.1 



1S.5 
38.2 

15S.S 
77.4 

304.0 



11.5 
4.9 
14.4 

12.7 
2.0 

25.3 
1.1 
2.2 

7.9 

12.2 

7.8 

20. S 



7.5 
tLB 
1.4 
6.1 
3.8 



3.455 

3.220 
2.092 

2.440 

2.755 

2.876 
3.120 

8.419 

2.603 
3.062 
2.567 
2.429 

3.133 
2.444 
2.814 

2.752 
2.650 
2.694 

3.125 
2.77" 
8.182 
2.961 

8.584 
3.132 

3.954 
3.221 



3.037 
2.5m; 
2.990 
3.125 
2.737 



9.2 


2.370 


6.3 


3.020 


4.7 


2.354 


•24.S 


2.553 


11.2 


3.129 



142 



APPENDIX. 



Si>;n and Name. 


S o 

5 


Discoverer. 


I 1 


31 


«i 


5 s 


a 


4< -2 

5 s 
'EL t 

C V 
C Qj 


3. "° 
g>fc 

>-l ° 


j 


S3 .2 


(166) Rhodope . . . 

(167) Urda 

(168) Sibylla 

(169)Zelia 

(170) 

U71) 
(172) 


1876 
1876 
1S76 
1876 

1S77 

1877 

1877 


Peters 


3.37 

4.22 
3.60 
2.67 

2.72 

3.52 
2.65 


2.07 
2.22 
3.15 
2.05 

2.38 

2.76 
2.11 


791.0 
614.5 
571.5 
979.9 

870. S 

636.8 
965.9 


Yrs. 
4.49 
5.7S 
6.21 
3.62 
4.08 

5.58 
3.68 


0.239 
0.312 
0.067 
0.131 
0.065 

0.121 
0.113 


O 

32.7 


o 
129.2 
170.1 
209.6 
354.6 
301.3 

101.9 
331.S 




11.7 
1.7 
4.6 
5.5 

14.3 

2.6 
10.0 


2.720 
3.21S 
3.37S 
2.35S 
2.551 

3.143 

2.3S1 




Watson 

Prosper Henry. 
Perrotiu 

Borelly 

Borelly 






REMARKS ON THE PRECEDING ELEMENTS OP THE PLANETS. 

Masses. — The masses of many of the planets are still very uncertain, 
because exact observations have not yet been made long enough to per- 
mit of their satisfactory determination. The mass of Mercury may be 
estimated as uncertain by £ of its entire amount j that of Mars by ^ ; 
those of Venus, the earth, Uranus, and Neptune by j^q ; while those of 
Jupiter and Saturn are probably correct to ioVo- 

The value of the earth's mass which we have given does not include 
that of the moon. The mass of the latter is estimated at gx^? that of 
the earth. 

The masses of Jnpiter, Saturn, Uranus, and Neptune which we have 
cited are all derived from observations of the satellites of these planets. 
The masses derived from the perturbations of the planets do not differ 
from them by amounts exceeding the uncertainty of the determinations. 
The most noteworthy deviation is in the case of Saturn, of which Le- 
verrier has found the mass to be ss^-q-q, a result entirely incompatible 
with the observations of the satellites. 

Diameters. — These are also uncertain iu many cases, especially in those 
of the outer planets, Uranus and Neptune. The densities which we have 
assigned to these last-mentioned planets, depending on their masses and 
diameters, must be regarded as uncertain by half their entire amounts. 

Elliptic Elements. — Of these it may be said that in general they are very 
accurate for the planets nearest the sun, but diminish in precision as we 
go outward, those of Neptune being doubtful by one or more minutes. 

Elements of the Small Planets. — These are only given approximately, in 
order that the reader may see the relations of the group at a glance. 
They are mostly taken from the Berliner Astronomisches Jahrbuch, which 
gives annually the latest elements known. The elements of the twenty 
or thirty last ones are very uncertain. 



DETERMINATIONS OF STELLAR PARALLAX. 



543 



VII. 



DETERMINATIONS OF STELLAR PARALLAX. 

THE following is a list of the stars the parallaxes of which are known 
to be investigated, with the results obtained by the different investiga- 
tors. The years are generally those in which the observations are sup- 
posed to have been made, but in the case of one or two of the earlier 
determinations they may be those of the publication of results. In tin- 
references the following abbreviations are used: 

A. G. Publicationen der Astronomischen GeeeVschaft. 

A.N. AstronomUche Nachrichten. 

B. M. Afonatsberichi (of the Berlin Academy of Sciences). 

C. K. Complex RenduB (of the French Academy of Sciences). 

D. O. Astronomical Observation, etc., at Dunrinsk, by Francis Briinnow. 

2 Parts. Dublin, 1870 and L874. 
Mel. Melanges MathimaUques et Astronomiques, Acodemit de St. Pe'ters- 

bourg. 
M.N. Monthly Notices of the Royal Astronomical Society. 
M. R. A. S. Memoirs of the Royal Astronomical Society. 
M. P. Memoires de V Academic de Sciences dt St. Pe'tersbourg. 
P.M. Reoueil des Memoires ties Astronomes de Poulkowa, publie' par W. 

Strum. St. P6tersbourg, 1853, vol. i. 
R. O. Radcliffe Observations, Oxford. 



Star's Name. 


Astronomer, and Date. 


Parallax. 


Probable 
Error. 


Reference. 


Groombridge ) 

No. 34 { 

Pole Star 

Capella 


( Anwers, from heliometer measures, ) 
( 1S63 '66 j 


0.292 

0.144 
0.075 
0.172 
0.147 
0.067 
0.025 
0.046 
0.305 
0.34 


±.036 

±.030 

± .018 

±.'20 
±.043 


B.M.,1867. 

P. M., p. G5. 

P.M.. p. 121. 
P.M.. p. 264. 
P.M., p. 136. 
Mel.. II., p. 400. 
P.M.. p. 04. 


Lindeiiau, from R. A.'s, 1750-1S1G 

W. Struve, Dorpat, lSls-'21 


Struve and Prenes, from R. A.'s,1822-' 3S 
Lundahl, from Dorpat declinations. .. 
Peters, from declinations, lS42-*44 


Peters, from declinations, 1842 

Struve, with Pulkowa equat., 1S55 







36 



544 



APPENDIX. 



Star's Name. 


Astronomer, and Date. 


Parallax. 


Probable 
Error. 


Reference. 1 




Maclear, 1S37 


0.16 
0.23 




M.R.A.S.,xi.,24S. 




( Henderson, from his own and Mac- [ 
( lear's observations j 




Gylden, from Maclear's obs., 1836-37. 


0.193 


±.087 


Mel., III., 595. 




Abbe, from Cape obs., 1856-'63 


0.273 


±.102 


M.N.,xxviii., p. 2. 




(Johnson, with Oxford heliometer,) 
( 1854-'55 j 


0.210 
0.133 


±.062 
±.106 


E. O., xvi.,p. (xi). 
P.M., p. 136. 


i UrsaeMaj 


Peters, from declinations, 1842 


Lalande No.) 
21185 ) 


Winnecke, with heliometer, 1857-68. . 


0.501 


±.011 


A. G., No. xi. 


Lalande No. ) 
21258 j 

Groombridge ) 
No. 1830 ... ) 


Auwers, 1860 '62 


0.271 
0.260 
0.226 


±.011 
±.020 
±.141 


A. N., No. 1411. 
M. N., xxiii., 173. 
P. M., p. 136. 


Krueger, 1862.(?) 


Peters, from declinations, 1842 




Faye, at the Paris Observatory 


1.08* 




C. R., xxiii. 




( Wichman, from Schliiter's observa-) 
1 tions, 1842-'43 j" 


0.180 


± .018 


A.N.,vol.36,p.29. 




Wichmanu, from his own obs., 1851t-j 


0.085 
0.089 


± .018 ' 
±.023 


j- lb., p. 33. 




Struve, 1847 '49 


0.034 
0.033 


±.029 
±.028 


P.M., p. 291. 
JR. O., xvi., p. 

1 (xxii). 


Johnson, with heliometer, lS54-'55.. . . 




Auwers, from Johnson's obs 


0.023 


±.033 


B. M., 1874. 




Bruunow, 1S70-'71 


0.09 


±.01 


D. O., II., p. 23. 

M N , xxiii , 173 


Oeltzen Arg. [ 


Krueger, 1862 (?) 


0.247 


±.021 


N., No. 17415) 
ft Centauri 


Moesta, from declinations, 1860-'64 . . . 


0.213 


±.069 


A. N., 16S8. 


a Bootis 


Peters, from declinations, 1S42 


0.127 


±.073 


P. M„ p. 136. 




Johnson, Oxford heliometer, 1845-'55. 


0.138 


±.052 


(R. O.. xvi., p. 
| (xxiii). 


a Centauri 


j Henderson, from his meridian obs. ) 
( at the Cape of Good Hope, 1832-'33. J 










a 1 Centauri, from right ascensions . . . 


0.92 


±.35 


^ 




a 1 Centauri, from direct declinations. 


1.42 


±.19 






a 1 Centauri, from reflected decs 


1.96 


±.47 


M. R. A. S., xi., 
| p. 67-68. 




a 2 Centauri, from right ascensions ... . 
a 2 Centauri, from direct declinations. 


0.48 
1.05 


±.34 

±.18 




a 2 Centauri, from reflected decs 


1.21 


±.64 








1.16 
1.14 


±.11 
±.11 


) 

P. M., p. 62. 


Peters, from the same obs., finds 




j Henderson, from Maclear's observa- ) 


0.913 




( M. R. A. S., xii., 




( tions, 1839-'40 [ 




i p. 370. 




Peters, from the same observations . . 


0.976 


±.064 


P.M., p. 63. 




Maclear, from decs., lS42-'44 and 1848. 


0.919 


±.034 


M.R.A.S.,xx.,98. 




Moesta, from declinations, 1860-64 . . . 


0.880 


±.068 


A. N., 1688. 


p Ophiuchi 


Krueger, 1S58 '59 


0.169 


±.010 


A. N., 1212. 





* This result is probably erroneous. 

t These results of Wichmann are parallaxes relative to the mean of certain stars of com- 
parison. He concluded that one of the latter had a large parallax which made the paral- 
lax of 1830 Gr. 0".72 ; but this view was afterwards proved wrong. 



DETERMINATIONS OF STELLAR PARALLAX. 



545 



j) Ophinchi 

.< Lyra 



a Cygni. 
61 Cygni, 



Astronomer, and Date. 

Krueger, 1858-'62 

Airy, Troughton's circle, 1836 

Airy, Jones's circle, l^iiO 

Strove, 183T-'40 

Peters, from declinations, 1S42 

Strove, L851-'S3 

Johnson, 1854-'55 

BrQnnow, 1868-'69 

Bruunow, l^To 

Peters, from declirrationB, H4-2 

(Bessel, with Konigsberg heliome-j 

1 ter, 183S J 

Bessel, from subsequent obs., 1840 

Peters, from declinations, 1842 

(Johnson, with Oxford heliometer, ( 

( 1852-'53 ) 

Anwers, from Johnson's obs 

Strove, lS52-'63 

Auwers.from Konigsberg heliometer. 



Parallax. 


Probable 
Error. 


Refan 


„ 


„ 




0.162 




A. X.. 1403. 


0.224 


) 


[M. a a. - 


-0.102 


) ■" 


1 ]). 269 


0.262 




P.M., 


0.103 


±.053 


P.M., p. 136. 


0.147 


± .009 


M. P., vii., vol. i. 


0.154 


±.040 




0.212 


±.010 


!>.<>.. Tart I. 




±.033 


D. <>.. PartIL 


-0.082 


±.043 


l'M..p. 130. 


0.314 






0.348 






0.349 




P.M.. p. 130. 


0.392 




R. O., vol. xiv. 


0.42 






0.500 


±.028 


M. P.. VII.. I., 45. 


0.664 


±.016 


A.N., 1411 -'10. 



546 APPENDIX. 



VIII. 

SYNOPSIS OF PAPERS ON THE SOLAR PARALLAX, 1854-"77. 

The following is believed to be a nearly complete list of the determi- 
nations of the solar parallax which have appeared since the discovery of 
the error of the old parallax in 1854. No papers have been included ex- 
cept those which relate immediately to the determination in question. 

1. Hansen, 1854—^.^. B. A. S., xv., p. 9. 
Statement that he finds the coefficient of the parallactic equation of the 
moon to be 125".705 — a value greater than that deduced from the solar 
parallax as given by the transits of Venus. 

2. Leverrier, 1858 — Annates de V Observatoire de Paris, iv., p. 101. 
Discussion of solar parallax from lunar equation of the earth, giving 
8".95. (In this paper Mr. Stone has found two small numerical errors : 
correcting them, there results 8".85. There is also a doubt about the 
theory, which might allow the result 8". 78.) 

3. Foucault, 1862 — Comptes Bendus, lv., p. 501. 
Experimental determination of the velocity of light, leading to the value 
of the solar parallax, 8".86. 

4. Hall, 1863 — Washington Observations for 1863, p. lx. 
Solar parallax, deduced from observations of Mars with equatorial in- 
struments, in 1862 : result, 8 // .8415. 

5. Ferguson, 1863 — Washington Observations for 1863, p. lxv. 
Solar parallax, deduced from observations with meridian instruments at 
Washington, Albany, and Santiago. Results various and discordant, ow- 
ing to incompleteness of the work. 

6. Stone, 1863— If. N. B. A. 8., xxiii., p. 183 ; Mem. B. A. S., xxxiii., p. 97. 
Discussion of fifty-eight corresponding observations of Mars (twenty-one 
pairs) at Greenwich, Cape, and Williamstown, leading to 8".943. 



SYNOPSIS OF PAPERS ON SOLAR PARALLAX, 1854-77. 547 

7. Hansen, 1863— M. N. 11. A. 8., xxiii., p. 243. 
Deduction of the value 8".97 from the parallactic inequality of the moon. 

8. Hansen, 1863— II. X. II. A. 8. f xxiv.. p. 8. 
A more accurate computatioo from the same data gives 8".9159. 

9. WlNNECKE, 1863— Artr. Nachr.,\ix., col. 261. 
Comparison of twenty-six corresponding observations (thirteen pairs) at 
Palkowa and the Cape of Good Hope. Parallax, 8".964. 

in. Powalky, 1864 Doctoral Dissertation, translated in Connaissana dea 

Temps, 1867. 
Discussion of the transit of Venn s, 1769. Result, 8".832, or B".86 when 
the longitude of Chappe's station is left arbitrary. 

n. Stone, 1867— M. X. R. A. S. f xxvii., p. 239. 
Attention directed to a slight lack of precision in Hansen's first paper 

(Xo. 7). Deduction also from its data of the result 8 .916 — agreeing with 
that from Hansen's second paper. 

1-2. Stone, 1867— M. N. Ii. A. S., xxvii.. p. 241. 
Correction of one of the numerical errors in Leven ier's determination. 
Result, 8".91. 

13. Stone, 1867—3/. X B. A. s.. xxvii.. p. 271. 
Determination of the parallactic inequality of the moon from 2075 ob- 
servations at Greenwich. Inequality. 125". 36. Solar parallax, 8 

14. Newcomb, 1867 — Washington Observations, 1865, Appendix II. 

Discussion of the principal methods employed in determining the solar 
parallax, and of all the meridian observations of Mars during the opposi- 
tion of 1862. Kesult, 8".848. 

15. Stone, 1867— M. X. J!. A. s.. xxviii.. p. 21. 
Comparison of Newcomb's and Leverrier's determinations of the solar 
parallax, leadiug to the detection of another small error in the latter. 

16. Stone, 1868— M. X. /?. A. >'.. xxviii.. p. 255. 
Rediscussion of the observations of the transit of Venus, 1769. Only 
observations of ingress and egress at the same station are used, and certain 
alterations are made in the usual interpretation of the observations by 
Ghappe in California, and Captain Cook aud his companions at Oraheite. 
The result of these alterations is that the parallax is increased to 8".91. 



5±S APPENDIX. 

17. Newcomb, 1868— M. N. P, A. S., xxix., p. 6. 
Criticism of Mr. Sterne's interpretation of Chappe's observation of egress 
in 1769. 

18. Stone, 1868— M. N. P. A. 8., xxix., p. 8. 
Reply to the preceding paper. 

19. Faye, 1869 — Comptes Pendus, lxviii., p. 42. 
Examination of the observations and interpretations in Mr. Stone's 

paper, concluding that all that we can decide from these observations is 
that the solar parallax is between 8".7 and 8".9. 

20. Stone, 1869— M. N. P. A. S., xxix., p. 236. 

Reply to Faye, criticism of Powalky's paper, and further discussions hav- 
ing for their object to show that the results of his paper agree with the 
scattered observations of ingress and egress in Europe and America. 

21. Anonymous, 1869 — Vierteljahrssclirift der Astr. Gesel., iv., p. 190. 
General review of recent papers on the solar parallax, dealing more 
especially with the work of Stone and Powalky. 

22. Powalky, 1870 — Astr. Nachr., lxxvi., col. 161. 

From a second discussion of the transit of Venus, 1769, he deduces 
8".7869. 

23. Powalky, 1871 — Astr. Nachr., lxxix., col. 25. 

From the mass of the earth as given by the motion of the node of Venus, 
8".77. But the adopted mass of Vet; us enters into the result in such a way 
as to make it decidedly uncertain. 

24. Leverrier, 1872 — Comptes Pendus, lxxv., p. 165. 
Determination of the solar j>arallax from the mass of the earth as derived 
from the motions of the planets, and the diminution of the obliquity of the 
ecliptic. Result, 8".86. (The distinguished author of this paper does not 
distinctly state in what way he has allowed for the fact that it is the com- 
bined mass of the earth and moon which is derived from the perturbations 
of the planets, while it is the mass of the earth alone which enters into the 
formula for the solar parallax. His presentation of the formulae seems to 
need a slight correction, which will diminish the parallax to 8".83.) 

25. Cornu, 1874-76 — Annates de V Observatoire de Paris, xiii. 
Redetermination of the velocity of light, leading to the parallax 8".794, 
if Struve's constant of aberration (20". 445) is used. 



SYNOPSIS OF V AVE US ON SOLAR PABALLAX, 1864-77. 54 !» 

26. Galle, 1875 — Breslau, Marttsctike $ Berendt. 
"Ueber einc Bestimmung der Sonnen Parallaxe aua correspondirenden 
Beobachtungen des Planeten Flora, im October and November 1873." Di«- 
cussion of observations made at nine northern observatories, and the Cape, 
Cordoba, and Melbourne, in the soul hern hemisphere. Result, 8".873. 

27. Puiseux, L875— Comptes Eendus, lxxx., p. 933. 
Computation of four contact observations of the transit of Venus in L874, 
made at Peking and St. Paul's Island. Result, -".-?;». 

28. Lindsay and Gill, 1877— .1/. .V. /,'. A. S., xxxvii.,p. 308. 
Reduction of observations of Juno with a heliometer at Mauritius, in 
1874. The result is 8".765; or 8".815 when a discordant observation is 

rejected. 

29. Lindsay and Gill, 1877 — Dunecht Observatory Publications, ii. 

Observations and discussion from which the preceding result is derived 
given in full. 

30. Aiky, 1877 — Government Report on the Telescopic Observations of the 
Transit of Venus. 

Observations of contacts made by the British expeditions, and prelimi- 
nary computation of the results for the solar parallax. The results given 
on page 7 are : 

From all the observations of ingress «-=8".738 IPf.=10.46 

From all the observations of egress ir=8".847 Wt,—2.B3 

Combined result ir=8' / .7S0 

31. Aiky, 1877— if. A'. B. ./. >.. xxxviii., p. 11. 
More complete discussion of the British observations leading to the 
mean result, 8".754. 

32. Stone, 1878— M. N. U. A. N., xxxviii.. p. 279. 
Another discussion of the observations contained in Airy's report (No. 
30) leading to the following entirely different results : 

From observations of ingress jr=8".S60±0".136X<! 

From observations of egress ir=S".9T9±0".a79X« 

From all tbe observations 7rrrS' / .SS4±0".123 xe 

33. Captain G. L. Tupmax. R. M. A.— IT. X 7?. A. S., xxxviii., p. 334. 
Statement that the treatment of ingress, as exhibited in the Parliament- 
ary Report, seemed unsatisfactory. The following are liis final results: 

From observations of ingress ir=8".857db©".040 

From observations of egress !r=8".792±0".027 

From all the observations tt=S".S13±0".033 

Note.— In the preceding list tbe abbreviation M. X. R. A. S. represents the Monthly 
Notices of the Royal Astronomical Society of London. 



550 APPENDIX. 



IX. 

LIST OF ASTRONOMICAL WORKS, MOST OF WHICH HAVE BEEN CON- 
SULTED AS AUTHORITIES IN THE PREPARATION OF THE PRESENT 
WORK. 

The following comprises : 1. A few of the leading works of the great 
astronomers of the past, and of the investigators of the present, arranged 
nearly in the order of time. In the case of works before 1800, the sup- 
posed date of composition, or the years within which the author flour- 
ished, are given. The list is presented for the benefit of those teachers 
and students who wish to be acquainted with these authorities, and can- 
not refer to such works as the BibliograpMe Astronomique of Lalande, or 
the Pulkowa Catalogus Librorum. 

2. Modern telescopic researches upon the physical aspects of the planets 
which have been employed in the preparation of Part III. of the present 
work. 

3. Recent works on special departments of astronomy, which may be 
useful to those who wish to pursue special subjects with greater fulness 
than that with which they are treated in elementary works. 

In the first two classes the selection is, for the most part, limited to 
works which have been consulted as authorities in the preparation of this 
treatise. In the case of Hevelius, however, some writings are added 
which I have not used, nor even seen, with the object of making the list 
of his larger works complete. Writings which have appeared in period- 
icals and the transactions of learned societies are necessarily omitted from 
the list, owing to their great number. 

The prices given for some of the older books are those for which they 
are commonly sold by antiquarian dealers in Germany. 

b.c. 250. Aristarchtjs : Be Magnitudinibus et Distantiis Soils et Lunce. Pisa, 
1572. $1. 

A.D. 150. Ptolemy, Claude : MErAAHS STNTA&EQS BIBA. ir, common- 
ly called The Almagest. 

The most recent edition is by the Abbe Halma, in Greek, with French 
translation. Two vols., 4to. Paris, 1813-'16. Commonly sells for 
$8 to $10. 



LIST OF ASTRONOMICAL WORKS. 55] 

880. ALBATEGNIUS: De Scientia Stellar •urn Liber. Bonn, 104.".. 

1543. Copernicus: De Bevolutionibns Orbhtm CaleeHum. 

The first edition of the great work of Copernicus is rare. The second 
(Basel, 1500) sells for *4. Two fine edition- have been published in 
Germany in recent times. Price $7 to $10. 

L597. Tycho Bbahe : AstrcnomuB Instauratm Meekaniea. tforifa 

1602. $'S. 
Contains description of Tycho's instruments and methods of observing. 
A8tronomia Instowrake Progymntumata. 

De Mundi Mtherei Recentioribus Phamomenis. Frank- 
fort, 1610. 

These two volumes generally go under the title of the former. A later 
edition (1648) was issued under the misleading title Opera Omnia. The 

selling price i> *<» for the two. 

1500- ) Kbpler, Johannes : Opera Omnia. Edidit Dr. Ch. Prisch. 

1630.) vols.,8vo. Frankfort, 1858-T1. 

A recent and complete edition of Kepler's voluminous writings. Price 
from s-jf) to s.;o. Generally cheaper at second-hand. 

1500- ) Galileo Galilei: Opere. L3 vols., 8vo. Milan, 1811. Price 

1636. ) about $10. 

A much better edition, published in 4to, about 1845, is more expensive. 
(ialileo wrote almost entirely in Italian. 

1603. Bayer, Johannes: Uranometria. 

Bayer's celebrated star-charts, in which the stars were first named with 
Greek letter-. Three or more edition- were published, the second be- 
ing in 1648, the third in lOC.l. s-J :>(>. 

Riccioli's: Almageatum Novum. 2 vols, in one, folio. Bonn, 1651. 

Aatronomia Beformata. Folio. Bonn, 1005. 

Two ambitious works, remarkable rather for their voluminousncss than 
for their value. The author being an eeelesia>tic. had to profess a dis- 
belief in the Copernican system. 

1630. BlTLLIALDUS : Astronomia Philolaioa. Folio. Paris. 1645. 

The last three works are cited as probably the most voluminous eom- 
pendiums of astronomy of the seventeenth century. They can all be 
purchased for $3 or $4 each. 

1611. Fabritii, J. : De Mdculia in Sole Observatia. 

1655. Borelli: De Vero Telescopic \ Inm tntore. Hague, 1655. 81. 



164 
1090 



> Hevelius. J. : Selenoffraphia. sive Luna Descriptio. Folio. 

The earliest great work on the geography of the moon and the aspects 
of the planets. Profusely illustrated. '84 to $5. 



552 APPENDIX. 

Hevelitjs, J. : Mercurins in Sole Visits. Folio, 1662. $1. 

Contains also Horrox's observation of the transit of Venus in 1639. 

Cometograpliia . Folio, 1668. 

The first great modern treatise on the subject of comets. 

Macliina Ccelestis, Pars Prior. Folio, 1673. 

Contains descriptions of his instruments, and a disquisition on the prac- 
tical astronomy of his time. 

MacMna Ccelestis, Pais Posterior. Folio, 1679. 



A very rare book, almost the entire edition having been destroyed by 
fire. A copy was sold for $50 in 1872. 



Annus Climactericus. Dantzic, 1685. 
Prodromus Astronomiw. Dantzic, 1690. 
Firmamentum Sobiescianum. Dantzic, 1690. 



These works comprise star-catalogues, star-maps, etc. $3 50. 

1659. Huyghens : Sy sterna Satumium. Hague, 1659. 

Horologium Oscillatorium. Paris, 1673. 

The latter work contains the theory of the pendulum clock. These two 
and most of the other important works of Huyghens were published 
in Leiden in 1751, under the title of Opera Mechanica, Oeometrica, As- 
tronomica et Miscellanea, nominally in four volumes, but the paging is 
continuous throughout the series, the total number of pages being 
776. Leiden, 1751. $5. 

1687. Newton, Isaac : PhilosopMw Naturalis Principia Mathematica. 4to. 

London, 1687. 

A number of editions of Newton's Principia have appeared. One of the 
most common is that of Le Seur and Jacquier, 3 vols, in 4. Geneva, 
1739. It is accompanied by an extended commentary. Sells for about 
$4. A very fine edition was issued in 1871, by Sir William Thomson, in 
Glasgow. There is also an English translation by Motte, which has 
gone through several editions in England and one in America. 

Brewster, Sir D. : Memoirs of the Life, Writings, and Discoveries 
of Sir Isaac Newton. 2 vols., 8vo. Edinburgh, 1855. 

1720. Flamsteed, J. : Historia Ccelestis Britanniea. 3 vols., folio. Lon- 
don, 1725. $10. 
Contains Flamsteed' s observations and star-catalogue. 

1728. Blanchini, F. : Hesperi et Phospliori nova Phwnomena sive Observa- 
tiones circa Planetam Veneris. Folio. Rome, 1728. 

1740. Cassini : Me'mens W Astronomic 4to. Paris, 1740. $1. 

1741. Weidler, Jo. : Historia Astronomioi. Small 4to. Wittemberg, 

1741. $2. 

Bernouilli, John : Opera Omnia. 4 vols., 4to. Lausanne, 1742. 

$5. 



LIST OF ASTRONOMICAL WORKS. 

Lk Moxxiki:: La Theoru des Cometes. 1 vol., 8vo. Pari-. 174:; 
|1. 

lTtiii. Kant, Immanuel : Schriften ear Phyeiecken Geographic. 

Leipzig, 1839. 

1780. I'im.kk: Comdtographie ; ou TraiU Historupu et Tkeoriqm det 

mites. •> vols.,4to. Paris, 17-:;. 

The most complete historical and general treatise on comets which has 
appeared. 

L780- ) Baillt : Histoire d* VAstronomu Ancienm depute son Origine jusqu'a 
17 ( Jo. $ VJ^tablissementdeV^colecPAlexandrie. lvol.,4to. Paris, 1781. 

ERstoin di VAstronomu Modern depms la Fondation d< 



VEeoli d?Alexandrie,jusqu'a VEpoqw de Mix. (XXX. 3 vols.. 4t<.. 
Paris, 1.779. |6. 
Traits' d< VAstronomu Indienm ei Orientate. 1 vol.. 4m. 



Paris, 17-7. 

These histories by Bailly are considered wry unbound, the aut 1 
in- a greatly exaggerated opinion of the knowledge of the ancients. 

1800. Lalande, J. De: Ribliographu Astronomique ; urn VHistom tk 
VAstovnomie depuis 1781 justju'a 1^2. 4to. Paris. l-<»:5. >:;. 

1.^17. Laplace, P. S. : Traitt de Mecanique Ctileste. 4 vols., 4to. Pari-. 

1799-1805. |60. 

This work is now expensive, all the editions being exhausted, 
edition is soon to be Issued. 

Exposition du System* du Monde. 1 vol., 4to. s*2. 

The latter work gives a very clear popular exposition of the laws of the 
celestial motions. 

Delambre: Histoiredi V Astronomic Ancienne. 2 vols., 4to. Paris, 
1-17. S4. 

Histoirede VAstronomie du Moyen Age. 1 vol., 4to. Paris, 



1819. |3. 



Histoirc <h V Astronomic Moderne. 2 vols., 4to. Paris. 



1S-21. $5. 

Histoire de V Astronomic on dix -huitiemc Steele. 1 vol., 4to. Paris, 

1827. |3. ♦ 

These histories by Delambre consist principally of abstracts of the writ- 
ings of all eminent astronomers, accompanied by a running commen- 
tary, but without any attempt at logical arrangement. Each work is 
taken up and passed' through in regular order, but it is only in the in- 
troductory essays that general views of the progress of the science arc 
found. 



554 APPENDIX. 

Encke, J. F. : Die Entfemung der Sonne von der Erde aus dem Ve- 
nusdurchgange von 1761 hergeleitet. 12mo. Gotha, 1822. 

Der Venusdurchgang von 1769. 12ino. Gotha, 1824. 

These two little books contain Eneke's researches on the solar parallax 
leading to the result 8". 5776, and the distance of the sun 95,300,000 
miles. 

Ideler, Dr. Ludwig : Handbuch der Mathematischen und Technischen 

Chronologic 2 vols., 8vo. Berlin, 1825. 

An exhaustive and commendable work on the measures of time adopted 
in various countries, especially in ancient times. 

Whewell, Wm. : History of the Inductive Sciences. London. 

Herschel, Sir John : Besults of Astronomical Observations made 
during the Years 1834, % % '7, '8, at the Cape of Good Hope. 1 
vol., 4to. London, 1847. 

Struve, F. G. W. : Etudes <jp Astronomic Stellaire. St. Petersburg, 

1847. 

Grant, Robert : History of Physical Astronomy, from the Earliest 
Ages to the Middle of the Nineteenth Century. 8vo. London, 1852. 

Biot, J. B. : Etudes sur VAstronomie Indienne et Chinoise. 8vo. 
Paris, 1862. 

Lovering, Joseph : On the Periodicity of the Aurora. Memoirs 
of the American Academy of Arts and Sciences. Boston, 1859 
and 1865. 

Oxbers, W., and Galle, J. G. : Die leichtste und bequemste Methode 

die Bahn eines Cometen zu berechnen. 8vo. Leipzig, 1864. 

This work contains a table of all orbits of comets computed, brought up 
to the end of 1863. 

Zollner, Dr. J. C. F. : Ueber die Natur der Kometen. 8vo. Leipzig, 

1872. 

Duhring, Dr. E. : Kritische Geschichte der Principien der Mechanilc. 
8vo. Berlin, 1873. 

Todhunter, I. : History of the Mathematical Theories of Attraction 
and the Figure of the Earth, from the Time of Newton to that of La 
Place. 2 vols., 8vo. London, 1873. 

II.— WORKS ON THE PHYSICAL ASPECTS OF THE PLANETS. 

Schroeter, J. H. : Beitrage zu den Neuesten Astronomischen Ent- 
deckungen. Herausgegeben von Bode. 3 vols., 8vo. Berlin, 1788- 
1800. $5. 



LIST OF ASTRONOMICAL WORKS. 555 

Schroeter, .1. IF.: Selenotopographisehe FragmeiUe zur gen an,-, ,, 
Kenntniss der Mondflaehe. 4to. Lilienthal, 1791. $3. 

Aphroditographisch* FragmenU ew genamern Kenntni 

Planeten Venus. 4to. Helmstedt, 1796. $6. 

Schroeter's Btyle was intolerably prolix and diffuse, so that a clear idea 
of the results he really attained involves no Bmall labor. 

Beer, W., and MXdt.br, J. H. : Physische Beobacktungen da Man 
bet seiner Opposition im September 1830. 12mo. Berlin. 1-:;". 

Der Mond nach seinen kosmisehen und mdividmeUen Ver- 

haltnissi a. oder Allgenu im verglewhend* Selenographie. 4n>. Berlin, 

1837. |7, 

Thi> volume is accompanied by a large map of the moon, and is the 
mOBl complete and celebrated work on selenography which hi 
appeared. 

Beer, W., and Madler, J. H. : Beitragt zur physiscken Kenntnis* 
der himmUsehen Eifrper im Sonnensysteme. 4to. Weimar. 1-41. 

Zollner: Photometrischt Untersuchungen mit besonderer Bucksiehi 
auf die physische Beschaffenheii der Bvnmelskorper. 8vo. Leip- 
zig, 1865. 

Engelmann: Ueber du Helligkeitsverhaltnisee der Jupiterstrabantm. 
8vo. Leipzig, 1871. 

Vogel, II. ('.. and Lohse : Beooachtungen angestellt auf der Stern* 
warte des Kammerherrn von Buloweu Bothkamp. 3 pts., 4to. Leip- 
zig, 1872-75. 

ux— recent treatises on special subjects. 

The Sun. 

Proctor, R. A. : The Sun : JRuln: Fire, Light, and Life of the Plan- 
etary System. 8vo. London, 1871. 

Lockyer, J. N. : Contribution* to Solar Physics. 8vo, London. 1874. 

Secchi, A. : Le Soleil 2 vols., 8vo, with Atlas. Paris. 1-T.V77 

The latter is the most complete and beautifully illustrated treatise on 
the sun which has yet appeared. 

The Moon. 
Nasmyth and CARPENTER : The Moon. London, L-T4. 
Contains very beautiful illustrations of lunar scenery. 
Proctor, R. A. : Hie Moon : Her Motions. Aspects. Scenery, and 

Physical Condition. Sxo. London. 1ST3. 
This work is illustrated with several of Mr. Rutherfurd's photographs. 






556 APPENDIX. 

Neison, Edmund : The Moon, and the Condition and Configurations 

of its Surface. Illustrated. 8vo. London, 1876. 
Principally devoted to selenography. 

Transits of Venus. 

Forbes, George : Transits of Venus. London, 1874. 

Proctor, R. A. : Transits of Venus. A Popular Account of Past 
and Coming Transits. 8vo. London, 1875. 



THEORETICAL AND PRACTICAL ASTRONOMY. 

Loomis, Elias : An Introduction to Practical Astronomy, with a Col- 
lection of Astronomical Tables. 8vo. New York, 1855. 
Contains much information for the amateur astronomer. 

Sa witch : Ahriss der Practischen Astronomie. 2 vols., 8vo. Ham- 
burg, 1850. 

Brunnow, F. : Practical and Spherical Astronomy. 8vo. London 
and New York, 1865. 

Chauvenet, W. : Manual of Spherical and Practical Astronomy. 2 

vols., 8vo. Philadelphia, 1863. 

The most complete and exhaustive treatise on the subject which has yet 
appeared. 

Watson, J. C. : Theoretical Astronomy. 8vo. Philadelphia, 1868. 



GLOSSARY OF TECHNICAL TERMS. 557 



X. 

GLOSSARY OF TECHNICAL TERMS OF FREQUENT OCCURRENCE IN 
ASTRONOMICAL WORKS. 

The following list is believed to include all the technical terms used in 
the -present work, as well as a number of others which the reader of as- 
tronomical literature will frequently meet with. The words in parenthe- 
ses which sometimes follow a term express its literal signification. 

Aberration (a wandering-away). Generally applied to a real or apparent 

deviation of the course of a ray of light. Especially (!) an apparent 
displacement of a star, owing to the progressive motion of light com- 
bined with that of the earth in its dibit, p. 21 1 : (2) the defects of action of 
a lens in not bringing all rays to the same focus. The spherical aberration 

of a lens results in the ravs which pass through the glass near its edge 
coming to a shorter foeus than those which pass near its centre, while 
the ohromatio aberration is the separation of the light of different colors. 

Achromatic (without <■<>!<>>■). Applied to an object-glass in which rays of 
different colors arc brought to the same focus, gee p. 114. 

Aerolite. A meteoric stone or other body falling from the celestial spaces. 

Albedo. Degree of whiteness, or proportion of incident light reflected by 
a non-luminous body. When the albedo of a body is said to be 0.6, it 
means that it reflects f% of the incident light. 

Alidade. A movable frame carrying the microscopes or verniers of a grad- 
uated circle. Not generally used in instruments of recent construction. 

Altitude. The apparent angular elevation of a body above the horizon, 
usually expressed in degrees and minutes. At the horizon the altitude 
is zero, at the zenith it is 90°. 

Annular (ring-shaped). Having the appearance or form of a ring. 

Anomaly. The angular distance of a planet from that point of its orbit 
in which it is nearest to the sun. or, in the ancient astronomy, to the 
earth. Draw two straight lines from the sun, oue to the nearest poiut 
of the orbit, or the perihelion, and the other to the planet, and the an- 
gle between these lines will be the anomaly of the planet. 

Anomalistic. Pertaining to the anomaly. The anomalistic year is the 
period between two consecutive returns of the earth to its perihelion. 
It is about 4' 15" longer than the sidereal year. 



558 APPENDIX. 

Ansas (handles). The apparent ends of the rings of Saturn, which look 
like handles projecting from the planet. 

Aperture of a Telescope. The diameter of the glass or mirror which 
admits the rays of light, clear of all obstacles. 

Aphelion. The part of the orbit of a planet in which it is farthest from 
the sun. 

Apogee. The point of an orbit in which the planet is farthest from the 
earth. In the ancient astronomy the planets were said to be in apogee 
when beyond the sun, and therefore at their greatest distance from the 
earth ; but the term is now applied only to the most distant point of 
the moon's orbit. 

Apsis (pi. Apsides). The two points of an orbit which are nearest to, and 
farthest from, the centre of motion, called, respectively, the lower and 
higher apsis. The line of apsides is that which joins these two points, 
and so forms the major axis of an elliptic orbit. The term is now near- 
ly superseded by the more special terms aphelion, perihelion, perigee, etc. 
See Elements. 

Armillary Sphere. A combination of circles used before the invention of 
the telescope for determining the relative directions or apparent posi- 
tions of the heavenly bodies on the celestial sphere. It is now entirely 
out of use. See p. 105. 

Astrolabe. A simple form of armillary sphere used by the ancient as- 
tronomers. 

Azimuth. The angular distance of a point of the horizon from the north 
or south. The azimuth of a horizontal line is its deviation from the 
true north and south direction. The azimuth of the east and west 
points is 90°. 

Binary System, A double star, in which the two components are found 
to revolve round each other. 

Binocular (two-eyed). Applied to a telescope or microscope in which both 
eyes can be used at once, as an opera-glass. 

Black Drop. A distortion of Mercury or Venus at the time of internal 
contact with the limb of the sun. See p. 179. 

Centesimal. Eeckoniug by hundreds. Applied to those denominational 
systems in which each unit is one hundred times that next below it. 
The centesimal division of the angle is one in which the quadrant is 
divided into 100 degrees or grades, the grade into 100 minutes, and the 
minute into 100 seconds. 

Chronograph (time-mark). An instrument for measuring time by mark- 
ing on a moving paper (see p. 155). Time is then represented by 
space passed over. 

Circle, Great. A circle which divides the sphere into two equal hemi- 
spheres, as the equator and the ecliptic. 



GLOSSARY OF TECHNICAL TERMS. 559 

Colures. The four principal meridians of the celestial sphere, all of which 
pass from the pole, and one of -which passes through each equinox, and 
one through each solstice. They mark the circles of h , 6 h , 12 h , and 18 h 
of right ascension, respectively. 

Conjunction (a joining). The nearest apparent approach of two heavenly 
bodies which seem to pass each other in their course. They arc com- 
monly considered as in conjunction when they have the same longitude. 
The term is applied especially in the case of a planet and the sun. The 
nearest approach is called superior conjunction when the planet is be- 
yond the sun, inferior when it is this side of it. Mercury and Venus 
are, of course, the only planets which can be in inferior conjunction. 

Cosmical. Relating to creation at large, in contradistinction to terres- 
trial, which relates to the earth. By a cosmical phenomenon is meant 
one which has its origin outside the earth and its atmosphere. 

Culmination. The passage of a heavenly body over the meridian of a 
place. This passage may be considered ;is occurring twice in a day, 
once above the pole, and again below it. twelve hours later. The for- 
mer is called the upper, the latter the lower, culmination. The upper 
culmination of the sun occurs at noon, the lower at midnight. 

Cusps (points). The pointed ends <>t' the seeming horns of the moon or 
of a planet when it presents the appearance of a crescent. 

Cycle (circle). A period of time at the end of which any aspect or rela- 
tion of the heavenly bodies recurs, as the Metonic cycle. 

Declination. The angular distance of a heavenly body from the equator. 
When north of the equator, it is said to be in north declination ; other- 
wise, in south declination. 

Deferent. In the ancient astronomy the mean orbit of a planet which 
was supposed to carry the epicycle. It is represented by the dotted 
circles in Figs. 10 and 11, pp. 38 and 39. 

Dichotomy (a cutting in two). The aspect of a planet when half illumi- 
nated, as the moon at first and last quarter. 

Digit. The twelfth part of the diameter of the sun or moon, formerly 
used to express the magnitude of eclipses. See p. 28. 

Dip of the Horizon. At sea, the depression of the apparent horizon be- 
low the true level, owing to the height of the observer's eye above the 
water. 

Direct Motion. A motion from west to east among the stars, like that 
of the planets in general. 

Eccentric. In the ancient astronomy, a circle of which the centre was 
displaced from the centre of motion. See p. 42, Fig. 13. 

Eccentricity. See Elements. 

Ecliptic. The apparent path of the sun among the stars, described iu 
Part I., Chap. I., § 3. See p. 13. 

37 



560 APPENDIX. 

Egress (a going forth). The end of the apparent transit of one body over 
another, when the former seems to leave the latter. 

Elements. In general, the data for predicting an astronomical phenome- 
non. Especially, the quantities which determine the motion of a plan- 
etary body. The independent elements of a planet are six in number, 
namely : 

1. The mean distance, or half the longer axis, AP, of the ellipse in which 
the planet moves round the sun, the latter being in the focus at S. 

2. The eccentricity, the ratio of the distance CS between the centre 
and focus of the ellipse to the mean distance. 

These two elements determine the size and form of the elliptic orbit 
of the planet. 




Fig. 112.— Diagram illustrating elliptic elements of a planet. 

3. The longitude of the ascending node, which gives the direction of 
the line in which the plane of the orbit intersects that of the ecliptic, or 
the angle which this line makes with the vernal equinox. 

4. The inclination of the plane of the orbit to that of the ecliptic. 

5. The longitude of the perihelion, P, for which is taken the longitude 
of the node, plus the angular distance from the node to the perihelion, 
as seen from the sun. 

These three quantities determine the position of the orbit in space. 

6. The mean longitude of the planet at some given epoch, or the time 
at which it passed the perihelion, P. 

To these six the time of revolution, or mean angular motion in a day 
or year, is usually added ; but as this can always be determined from 
the mean distance, and vice versa, by Kepler's third law, the two are not 
regarded as independent elements. 

The quantities we have described are usually represented by algebraic 
symbols, as follows : 

a, the mean distance. 1 5 or n, the longitude of the perihelion. 

e, the eccentricity. e, the mean longitude at some epoch. 

or fi, the longitude of the node. n, the mean motion. 

i or </>, the inclination. I a>, the distance from node to perihelion. 



GLOSSARY OF TECHNICAL TERMS. 561 

Ellipticity. Deviation from a truly circular or spherical form, so as to 
become an ellipse or spheroid. An orbit is said to be more elliptic the 
more it deviates from a circle. 

Elongation. The apparent angular distance of a body from its centre of 
motion, as of Mercury or Venus from the sun, or of a satellite from its 
primary. 

Emersion (a coming out). The reappearance of an object after being 
eclipsed or otherwise hidden from view. 

Ephemeris. A table giving the position of a heavenly body from day to 
day, in order that observers may know where to look for it. Applied 
also to an astronomical almauac giving a collection of such tables. 

Epicycle. In the ancient astronomy, a small circle the centre of which 
moves round on the circumference of a larger one, especially the circle 
in which the three outer planets seemed to perform an annual revolu- 
tion in consequence of the revolution of the earth around the sun. 

Equation of the Centre. The angular distance by "which a planet mov- 
ing in an ellipse is ahead of or behind the mean position which it 
would occupy if it moved uniformly. It arises from the eccentricity of 
the ellipse, vanishes at perihelion and aphelion, and attains its greatest 
value nearly half-way between those points. 

Equation of Time. See p. 1C4. 

Equator. The great circle half-way between the two poles in the earth 
or heavens. The celestial equator is the line EF in Fig. 3, p. 12. See 
also pp. 62, and 146,147. 

Equatoreal. A telescope mounted so as to follow a star in its apparent 
diurnal course, as described on p. 119. 

Equinox. Either of the two points in which the sun, in its apparent an- 
nual course among the stars, crosses the equator. So called because the 
days and nights are, when the sun is at those points, equal. 

Evection. An inequality in virtue of which the moon oscillates about 
1£° on each side of her mean position in a period of 31 days 19 hours. 

Eye-piece, of a telescope. The small glasses nearest to the eye, which 
magnify the image. See pp. 110 and 118. 

Faculee (small torches). Groups of small shining spots on the surface of 
the sun which are brighter than other parts of the photosphere. They 
are generally seen in the neighborhood of the dark spots, and are sup- 
j)osed to be elevated portions of the photosphere. 

Filar (made of thread). Applied to micrometers made of spider lines. 

Focus (a fireplace). A point in which converging rays all meet. The 
focus of a telescope is the point at which the image is formed. See p. 109. 

Geocentric. Referred to the centre of the earth. The geocentric posi- 
tion of a heavenly body is its position as seen or measured from the 
earth's centre. 



562 APPENDIX. 

Geodesy. The art or science of measuring the earth without reference 
to the heavenly bodies. 

Gnomon. In the old astronomy, the style of a sundial or any object the 
shadow of which is measured in order to learn the position of the sun. 

Golden Number. The number of the year in the Metonic cycle, counted 
from 1 to 19. See p. 48. 

Heliacal {relating to the sun). Applied in the ancient astronomy to those 
risings or settings of bright stars which took place as near to sunrise 
or sunset as they could be observed. 

Heliocentric. Referred to the sun as a centre. Applied to the positions 
of the heavenly bodies as seen from the sun's centre. 

Heliometer. An instrument in which the object-glass is sawed into two 
equal parts, each of the parts forming an independent image of a heav- 
enly body in the focus. When the two parts are together in their origi- 
nal position, these images coincide, but by sliding one part on the other 
they may be separated as far as is desired for the purposes of measure- 
ment. It is much used in Germany for measuring distances too great 
for the application of a filar micrometer. 

Heliostat. An instrument in which a mirror is moved by clock-work in 
such a way as to reflect the rays of the sun in a fixed direction, notwith- 
standing the diurnal motion. 

Heliotrope. An instrument invented by Gauss for throwing a ray of sun- 
light in the direction of a distant station. It is much used in geodetic 
measurements. 

Hour Angle. The distance of a heavenly body from the meridian, meas- 
ured by the angle at the pole. It is commonly expressed in time by the 
number of hours, minutes, etc., since the body crossed the meridian. 

Immersion (a plunging in). The disappearance of a body in the shadow 
of another, or behind it. 

Inclination, of an orbit. See Elements. 

Ingress (a going in). The commencement of the transit of one body over 
the face of another. 

Latitude. The angular distance of a heavenly body from the ecliptic, as 
declination is distance from the equator. 

Libration (a sloiv swinging, as of a balance). The seeming slight oscillations 
of the moon around her axis, by which we sometimes see a little on one 
side of her, and sometimes on the other. 

Longitude. If a perpendicular be dropped from a body to the ecliptic, its 
celestial longitude is the distance of the foot of the perpendicular from 
the vernal equinox counted towards the east. 

Lunation. The period from one change of the moon to the next. Its 
duration is 29^- days, or, more exactly, 29.5305879 days. 

Mass, of a body. The quantity of matter contained in it, as measured 



GLOSSARY OF TECHNICAL TERMS. 563 

by its weight at a given place. Mass differs from weight in that the 
latter is different in different places even for the same body, depending 
on the intensity of gravity, whereas the mass of a body is necessarily the 
same everywhere. 

Mean Distance. See Elements. 

Meridian. The terrestrial meridian of a place is the north and south 
vertical plane passing through that place, or, the great circle in which 
this plane intersects the celestial sphere. It passes through the pole, 
the zenith, and the north and south points of the horizon. Celestial 
meridians are great circles passing from one pole of the heavens to 
the other in all directions, as shown in Fig. 45, p. 147. Every celes- 
tial meridian coincides with the terrestrial meridian of some point on 
the earth. 

Metonic Cycle. See p. 48. 

Micrometer (small measwer). Any instrument for the accurate measure- 
ment of very small distances or angles. 

Nadir. The point of the celestial sphere directly beneath our feet. or the 
direction exactly downwards. 

Node. The- point in which an orbit intersects the ecliptic, or other plane 
of reference. See Elemmts t and p. 33. 

Nutation. A very small oscillation of the direction of the earth's axis. 
It arises from the fact that the forces which produce the precession of 
the equinoxes do not act uniformly, and may therefore be considered as 
the inequality of precession arising from the inequality of the force 
which produces it. 

Oblate. Applied to a round body which differs from a sphere in being 
flattened at the poles, as in the case of the earth. 

Obliquity of the Ecliptic. The inclination of the plane of the equator 
to that of the ecliptic, which is equal to half the difference between the 
greatest meridian altitude of the sun, which occurs about June 21st, and 
the least, which occurs about December 21st. At the beginning of 1850 
its value was about 23° 27^', and it is diminishing at the rate of about 
47" per century. 

Occultation (a hiding). The disappearance of a distant body through the 
interposition of a nearer one of greater angular magnitude. Applied 
especially to the case of the moon passing over a star or planet, and to 
that of Jupiter hiding one of his satellites. 

Opposition. The relation of two bodies in opposite directions. The 
planets are said to be in opposition when their longitude differs 180° 
from that of the sun, so that they rise at sunset, and set at sunrise. 

Orbit. The path described by a planet around the sun, or by a satellite 
around its x>rimary planet. 

Parallax. The difference of direction of a heavenly body as seen from 



564 APPENDIX. 

two points, as the centre of the earth and some point on its surface. 

See Part II., Chap. III., § 1. 
Parallels. Imaginary circles on the earth or in the heavens parallel to 

the equator, and having the pole as their centre. The parallel of 40° N. 

is one which is everywhere 40° from the equator and 50° from the north 

pole. See Fig. 45, p. 147. 
Penumbra. A partial shadowing. Applied generally in cases where 

light is partially, but not entirely, cut off. 
Peri- (near). A general prefix to denote the point at which a body revolv- 
ing in orbit comes nearest its centre of motion; as, perihelion, the point 

nearest the sun; perigee, that nearest the earth; peri -Saturnium, that 

nearest the planet Saturn, etc. 
Perturbation. A disturbance in the regular elliptic or other motion of a 

heavenly body, produced by some force additional to that which causes 

its regular motion. The perturbations of the planets are caused by 

their attraction on each other. 
Photometer (light-measurer). An instrument for estimating the intensity 

of light. The number of kinds of photometers is very great. 
Precession of the Equinoxes. A motion of the pole of the equator 

around that of the ecliptic in about 26,000 years. See pp. 19, 62, 88. 
Prime Vertical. The vertical circle passing due east and west through 

the zenith, and therefore intersecting the horizon in its east and west 

points. 
Quadrature. The positions of the moon when she is 90° from the sun, 

and therefore in her first or last quarter. 
Radiant Point. That point of the heavens from which the meteors all 

seem to diverge during a meteoric shower. See p. 390. 
Refraction (a breaking). The bendiog of a ray of light by passing through 

a medium. Astronomical refraction means the refraction of the light of a 

heavenly body caused by the atmosphere, as described on p. 300. 
Retrograde (backward). Applied to the motion of a planet from east to 

west among the stars. 
Saros. A period or cycle of 18 years 11 days, in which eclipses recur. 

See p. 30. 
Scintillation (a twinkling). The twinkling of the stars. 
Secular (relating to the ages). Applied to those changes in the planetary 

orbits which require immense periods for their completion. See p. 95. 
Selenography. A description of the surface of the moon, as geography is 

a description of the earth's surface. We might call it lunar geography 

but for the etymological absurdity. 
Sexigesimal. Counting by sixties. Applied to those denominate sys- 
tems in which one unit is sixty times the next inferior one, as the usual 

subdivision of time and arc. 



GLOSSARY OF TECHNICAL TERMS. 565 

Sextant. The sixth part of a circumference. Also an instrument much. 
used in practical astronomy and navigation, for the read y measurement of 
the angular distance of two points, or of the altitude of a heavenly body. 

Sidereal. Relating to the stars. Sidereal time is time measured by the 
diurnal revolution of the stars. Each unit of sidereal time is ahout 
^V^th part shorter than the usual one. See p. 150. 

Signs of the Zodiac. The twelve equal parts into which the ecliptic or 
zodiac was divided by the ancient astronomers. These signs, begin- 
ning at the. vernal equinox, are: 



Aries, the Ram. 
Taunts, the Bull. 
Gemini, the Twins. 
Cancer, the Crab. 
Leo, the Liou. 
Virgo, the Virgin. 



Libra, the Balance. 
Scorpius, the Scorpion. 
Sagittarius, the Archer. 
Capricornus, the Goat. 
Aquarius, the Water-bearer. 
Pisces, the Fishes. 



Solstices (standing-points of the sun). Those points of the ecliptic which 
are most distant from the equator, and through which the sun passes 
about .June 21st and December 21st. So called because the sun. having 
then attained its greatest declination, stops its motion in declination, 
and begius to return towards the equator. The two solstices are desig- 
nated as those of summer and winter respectively, the first being in 6 
hours and the second in 18 hours of right ascension. 

Sothic Period. That in which the Egyptian year of 365 days correspond- 
ed in succession to all the seasons. The equinoctial year being supposed 
to be 365J days, this period would be 1461 years, but it is really longer. 
See p. 47. 

Speculum (a mirror). The concave mirror of a reflecting telescope. 

Stationary. Applied to those aspects of the planets occurring between 
the periods of direct and retrograde motion when they appear for a short 
time not to move relatively to the stars. 

Synodic. Applied to movements or periods relative to the sun. The 
synodic movement of a planet is the amount by which its motion ex- 
ceeds or falls short of that of the earth round the sun, while its synodic 
period is the time which elapses between two consecutive returns to 
inferior or superior conjunction, or to opposition. 

Syzygy. The points of the moon's orbit in which it is either new moon or 
full moon. The line of the syzygies is that which passes through these 
points, crossing the orbit of the moon. 

Terminator. The bounding line between light and darkness on the moon 
or a planet. 

Transit (a passing across). The passage of an object across some fixed line, 
as the meridian, for example, or between the eye of an observer aud an 
apparently larger object beyond, so that the nearer object appears on 
the face of the more distant one. Applied especially to passages of Mer- 



566 APPENDIX. 

cnry and Venus over the disk of the sun, and of the satellites of Jupiter 
over the disk of the planet. 

Trepidation. A sIoav oscillation of the ecliptic, having a period of 7000 
years, imagined by the Arabian astronomers to account for the discord- 
ance in the determinations of the precession of the equinoxes. In con- 
sequence of this motion the equinox was supposed to oscillate backward 
and forward through a space of about twenty degrees. The trepidation 
continued to figure in astronomical tables until the end of the sixteenth 
century, but it is now known to have no foundation in fact. 

Umbra (a shadow). That darkest part of the shadow of an object where 
no part of the luminous object can be seen. Also, the interior and dark- 
est part of a sun-spot. 

Vertical, Angle of. The small angle by which the real direction of the 
earth's centre from any point on its surface differs from that which is 
directly downward, as indicated by the plumb-line. It arises from the 
elipticity of the earth, vanishes at the equator and poles, and attains its 
greatest value of about 12' at the latitude of 45°. 

Vortex (a ivhirlpool) ; pi. Vortices. The theory of vortices is that which 
assumed the heavenly bodies to be carried round in a whirling fluid. 
See p. 72. m 

Zenith. The point of the celestial sphere which is directly overhead, and 
from which a plumb-line falls. The geocentric zenith is the point in which 
a straight line rising from the centre of the earth intersects the celestial 
sphere. It is a little nearer the celestial equator than the apparent or 
astronomical zenith, owing to the ellipticity of the earth. See Vertical, 
Angle of. 

Zodiac. A belt encircling the heavens on each side of the ecliptic, within 
which the larger planets always remain. Its breadth is generally con- 
sidered to be about sixteen degrees — eight degrees on each side the 
ecliptic. In the older astronomy it was divided up into twelve parts, 
called signs of the zodiac. 



INDEX 



PAGE 

Abbe, distribution of the nebulae 4G0 

parallax of Sirius 544 

A berration of light described 213 

Acceleration of moon's motion 96 

Adams determines moon's acceleration. 90 

investigates motions of Uranus 3GS 

Aerolites, description of «94, 39G 

Airy, his water telescope '210 

density of the earth 4G 

Algol a variable star 434 

Apparition, circle of perpetual 11 

Argelander catalogues the stars 122 

Argus, »), a variable star 436 

Aristarchus attempts to measure the dis- 
tance of the sun 22 

Asten, motion of Encke's comet 390 

Asteroids (see also Planets, small). . 329, 538 

Astrolabe described 107, 55S 

Astronomer Itoyal, duties of 162 

Attraction of a mountain S5 

of small masses 81 

Aurora, description of. 309 

height, nature, etc 310 

periodicity of 255 

spectrum of. 311 

.1 timers, motion of Sirius and Procyon. . 447 

Baily determines density of earth 84 

Baily-s beads explained 314 

Barker, spectrum of Aurora 311 

Bayer system of naming stars 423 

Bernoulli (J.) sustains theory of vortices. 80 

Bessel, parallax of 61 Cygni 20S 

Black drop in transits of Venus 181 

its cause 183 

Blanchini, his great telescope 114 

rotation of Venus 297 

Bocie's law of planetary distances 237 

Bond discovers satellite of Saturn 358 

intensity of moonlight 323 

investigates rings of Saturn 358 

Books, list of, for reference 550 



FAG* 

Bradley attacks stellar parallax 206 

detects aberration of light 213 

Brake (Tycho), his obs. and system 06 

lln'iniidir, researches in stellar parallax. 810 

Calendar, history, etc 44 

Julian and Gregorian 49 

Cassegrainian telescope 126 

Cassini discovers satellites of Saturn . . . 360 

theory of Saturn's rings 358 

Cavendish, density of the earth 92 

Cayley determines moon's acceleration. 98 

Challis searches for Neptune 

Chromosphere of the sun 982 

its violent movements, etc 268 

Clt ronograph described 157 

Circles of the celestial sphere L4B 

Clark (Alvan), his telescopes 139 

discovers companion of Sirius 14*> 

Clusters of stars 449 

Comet, great, of 1680 382 

ofl682(Halley's) 383 

oflS43 387 

its near approach to sun. . 265 

of 1858 (Donati's) 387 

views of 376, 388 

of Biela 3S6, 404 

of Eucke 3S9 

Comets, aspects of, etc 373 

development 374 

relations to meteors 399 

motions 377 

number 3S1 

orbits of, their form 377 

physical constitution of. 406 

remarkable, description of. 3S2 

tails of, repelled by the sun 408 

Constellations, antiquity of names 422 

description of. 425 

Copernicus founds modern astronomy. . 51 

publishes his system 53 

his system explained 54 



568 



INDEX. 



PAGE 

Copernicus rep. eccentricity of orbits 60 

his distances of the planets 60 

estimate of his work 61 

work condemned by Inquisition 72 

Comu measures velocity of light 220, 222 

Corona of the sun described 258 

its probable nature 264 

its spectrum 263 

Cosmogony, the system of 499 

Cycle, the Metonic 48 

Dean determ. transatlantic longitude.. . . 161 
Delaunay, secular acceleration of moon. 97 

Density of the earth 84 

Descartes' theory of vortices 72 

Donates comet, description of 387 

views of. .376, 388 

Draper, his great telescope 137 

photograph of the moon 319 

theory of the solar spectrum 232 

Earth, density of. 84 

elements of orbit.. 536 

figure of, view of Ptolemy 32 

on Newton's theory 86 

the French investigations. 87 

theory of its fluidity 305 

difficulties of this theory 306 

temperature of interior 304, 519 

secular cooling of. 519 

Easter, how determined 4S 

Eastman, view of total eclipse in 1869 . . 259 

Eccentric in ancient astronomy 41 

Eclipses, geometrical explanation 24 

classification 25 

duration of. 28 

ancient observations of. 257 

seasons and periodic recurrence 29 

total, phenomena of 258 

of 1869, general view of 259 

observations of 263 

Ecliptic, description of 15 

obliquity explained 61 

Elements of the planetary orbits 536, 560 

Encke determines solar parallax 183 

investigates resisting medium 387 

Epicycles, ancient system of 37 

explained by Copernicus 54 

Equator, celestial 12, 149 

Evection discovered by Ptolemy 43 

Eye-piece of telescope 120 

Faculce of the sun 561 

Faye, constitution of the sun 279 

his comet, motions of 391 

Fizeau measures velocity of light 219 

Foucault measures velocity of light 220 



PAGE 

Galaxy, or Milky Way, its aspect 424 

Galileo reinvents the telescope 10S 

discovers phases of Venus 296 

satellites of Jupiter 344 

resolves the Milky Way 416 

Galle, parallax of asteroids 202 

optical discoverer of Neptune 369 

Gentil, his unfortunate voyage .182 

Gilliss, expedition to Chili 176 

Glacial epoch, its possible cause 247 

Glasenapp, velocity of light 216 

Gnomon, its use by the ancients 106 

Golden number 48 

Gould determ. transatlantic longitude . . 161 

Gravitation not newly discovered 48 

how generalized by Newton 76 

universal law of 81 

exerted by small masses 81 

explains motion of the planets . . .98, 102 
Grubb constructs Melbourne telescope.. 134 

Hall observes spot on Saturn 349 

discovers satellites of Mars 329, 331 

Halley discovers secular accel. of moon. 96 

total eclipse in 1715 258 

periodicity of his comet 383 

proposes obs. of transit of Venus.. . . 178 

Hansen, moon's secular acceleration 97 

solar parallax 184 

Harkness, spectrum of the corona 263 

observes meteoric shower 397 

Herschel, his telescopes 12S 

discovery of Uranus 362 

of two satellites of Uranus 363 

his star gauges 474 

structure of the universe 476 

nebular hypothesis.. 503 

Song of the Telescope 129 

Hilgard determ. transatlantic longitude. 161 
Hipparchus observes motions of planets 40 

catalogues the stars 421 

Holden investigates satellites of Uranus. 365 

Hooke, problem of stellar parallax 205 

Horrox first observes transit of Venus . . 177 
Huggins, appearance of suu's surface . . . 243 

motion of stars in line of sight 464 

spectrum of nebulae 455 

of new star 443 

Huyghens prep, the way for gravitation. 73 
discovers rings of Saturn 350 

Inquisition condemns work of Coper- 
nicus 72 

Intra-Mercurial planets, supposed. . .102, 2S7 
pretended observations of 293 

Jansen, supposed inventor of telescope.. 109 



INDEX. 



569 



, PAGE 

Janssen analyzes solar protuberances. . . 260 
photographs of the sun 244 

Jupiter, the planet 339 

appearance of surface 340 

elements of orbit 53G 

light and activity of 342 

rotation of, on axis 343 

satellites of 344 

Kant, structure of the universe 470 

founds nebular hypothesis 501 

Kepler investigates motions of planets. OS 
first two laws of planetary motion.. 69 

third law 70 

structure of the universe 469 

Lambert, structure of the universe 473 

Lcmglep, appearance of the sun 242 

heat of the sun 243 

on the sun's constitution 286 

Laj)lace, cause of moon's acceleration. . . 96 

nebular hypothesis 503 

Lassell, his great telescopes 133 

discovery of satellites 364, 372 

Latitude, how dcterm. astronomically. . . 150 
Leverrier investigates motion of Mercury 102 

discovery of Neptuue 367 

Libration of the moon 313 

Light, motion of 21^ 

time of coming from sun 215 

velocity of, measured 217 

Lipperhcy an inventor of the telescope . 109 
Lockycr analyzes sun's protuberances. . . 261 
Longitude, terrestrial, how found 152 

the transatlantic 161 

Loomis, periodicity of the aurora, etc. . . 255 

Lovering, periodicity of the aurora 255 

Lyman investigates atmosphere of Venus 300 

Mars, the plauet 326 

aspect of. 327 

elements of orbit 536 

maps of 328, 329 

rotation of. 32S 

satellites of. 537 

Maxkelyne, attraction of mountain S5 

Maxwell, theory of Saturn's rings 358 

Mercury, the planet 2S9 

elements of orbit 536 

ancient theory of 40 

aspect and rotation 290 

motion of perihelion 102, 292 

transits of 291 

Meridian circle described 154 

Meteoric showers 393 

radiant point of 39S 

produced by comet ... 404 



PAGE 

Meteors ana' shooting-stars 392 

how caused 395 

combustion of, by motion 396 

orbits of 402 

relations to comets 399 

Metonic cycle 48 

Milky Way described 424 

Moller, motion of Faye's comet 391 

Mouth, origm of 4.V47 

Moon, revolution and phases 21 

acceleration of its motion 96 

unexplained changes of motion 98 

path among the stars 23 

nodes, motion of. 23 

eclipses of, how caused J4 

gravitation of, found by Newton 76 

investigations of the ancients 4S 

atmosphere 320 

surface described 317 

distance and magnitude 312 

figure, rotation, and libration 313 

changes of surface 

light and heat of. 323 

effect ou the earth 

Music of the spheres 4 

Ndsmyth, appearance of the sun 242 

Xebulce, appearance of 45_' 

views of. 156, 4. r .- 

distribution 458 

great, of Orion 453 

gaseous nature of. 455 

Nebular hypothesis 501 

reached by reasoning back- 
ward from the present. . . 507 

conclusions respecting 522 

Neptune, history of its discovery 300 

elements of orbit 536 

physical aspect of. 372 

satellite of 372 

Xeicall, his great telescope 140 

Newton (H. A.), meteoric showers 399 

Xeicton (Sir I.), his work 74 

laws of motion 75 

theory of comets 410 

Olbers, hypothesis of the explosion of a 

planet 332, 334 

Orbits of the planets 536, 53S 

Parallax; definition of 107 

annual 172 

solar, measures of 173 

from transit of Venus 177 

most probable value 202 

list of papers on 545 

stellar, efforts to find 204 



570 



INDEX. 



Parallax, list of measures 543 

Peirce, rings of Saturn 358 

perturbations of Neptune 371 

theory of comets 411 

Photosphere, its appearance 242 

light and probable nature 269 

Pickering, intensity of sunlight 245 

Planets, the seven, of the ancients 14 

order of distance, ancient 40 

modern 235, 239 

laws of their motion 09, 93 

secular variations of orbits 95 

aspects of. 239 

distances and masses 237 

of other suns 524 

supposed intra-Mercnrial 102 

small, fill gap between Mars and Ju- 
piter 331 

earlier discoveries 332 

number and mass 336 

elements of orbits 53S 

Pleiades, map of. 450 

Plurality of worlds : 524 

Pole of the heavens 10 

Precession of the equinoxes 19 

explained by Copernicus 62 

cause of 88 

Proctor, arrangement of the stars 4S4 

Prominences. See Protuberances. 

Protuberances of the sun 258 

spectroscopic observation of 260 

Ptolemy, his system of the world 32 

his answers to objectors 35 

his relations to Copernicus 5S 

his catalogue of stars 421 

Pythagoras, crystalline spheres of 3 

his supposed system 4, 52 

Radiant point of meteors 398 J 

Refraction, astronomical 306 

Reich, density of earth 84 

Resisting medium, indications of 389 

researches relating to 390 

Rings of Saturn 349 

Rittenhouse observes transit of Venus . . 300 

Roemer searches for stellar parallax 205 

Ros.se, his great telescope 133 

heat of the moon 324 

Rutherford, photographic measurements 1S6 

Saros, or period of eclipses 30 

Satellites of Jupiter 344 

of Saturn 359 

of Uranus 363 

of Neptune 372 

Saturn, the planet 346 

aspect of 347 



PAGE 

Saturn, elements of orbit 536 

rotation on axis 34S 

remarkable spot on 349 

rings 349, 358 

old views of 351 

phases of 352 

satellites of 359 

Schiaparelli theory of meteors 401 

Schonfeld catalogue of variable stars ... 437 

Schwabe, periodicity of sun-spots 254 

Seasons, explanation of 63 

Secchi, temperature of the sun 247 

on the sun's constitution 271 

view Of lunar crater 321 

spectrum of nebula 455 

Secondary spectrum in telescope 240 

Seidel, photometric researches 421 

Sirius, brilliancy of 421 

companion of. 447 

Solar system, relation to the stars 103 

structure of. 235 

plan of 240 

Spectroscope described 225 

Spectrum analysis explained 229 

Sphere, celestial, described 7 

circles of 148 

Spheres, crystalline, of Pythagoras 3 

Stars (see also Universe) 415 

arrangement of, in space 46S, 4S6 

binary systems of. 446 

catalogues of 421 

changes among them 467 

clusters of 449 

constellations, formation of. 422 

description of. 425 

double 444 

light of, how graded 419 

magnitudes of, apparent 418 

intrinsic 491 

number of, visible 418 

motions of. apparent 460, 492 

in line of sight 464 

names of, how given 423 

nearest * 209 

new, explanation of 438 

nature of 441 

observations of some 440 

parallaxes of 204, 543 

probable orbits of some 4S4 

systems of 484 

shooting. See Meteors. 

variable 434 

Stone corrects solar parallax 201 

Struve (O.), changes in rings of Saturn. . 355 

inner satellites of Uranus 364 

Struve (W.) investigates stellar parallax. 207 
parallax of a Lyras 209 



INDEX. 



571 



PAGE 

Struve (W.), structure of the Universe. . . 4S2 

Sun, age of 517 

appearance of 241 

atmosphere of 240 

constitution of 264 

brightness of, as a star 4itl 

contraction of, probable 515 

distance of, most probable value of. 202 

distance of, methods of rinding 1% 

gaseous theory of. 270 

heat of, quantity radiated 247 

how maintained 253, 513 

law of radiation 509 

motion, apparent annual 14 

probable real 402 

parallax, how measured 173-203 

most probable value 203 

list of papers on 540 

rotation on axis, law of 255 

spots, their appearance 24S 

their periodicity 254 

appear as cavities 251 

surroundings of. 257 

temperature -'47 

Telescope, origin of 108 

Galilean form of 110 

principle of construction of 110 

magnif ying power of 112, 141 

aberration, defect of 112 

achromatic 116 

how mounted for use 120 

reflecting, how made 123 

great ones of modern times 127 

list of the principal 529 

Thomson, rigidity of the earth 304 

Tides, how produced 90 

friction of, retards earth 98 

Time, mean and apparent 164 

sidereal 152 

See also Calendar. 

Titvs, law of planetary distances 269 

Transits of stars, how observed 156 

of Venus, law of recurrence 177 

old observations ISO 

inlS74 1S5, 192 

in 1SS2, where visible 196 



PAGE 

Transits of Mercury 

Tycho Brake, his work Oo 

I 'i<"jh neigh, catalogue of stars 421 

Universe, structure of. 

stability of, not necessary 408 

Uranus, the planet 3C1 

elements of orbit 

old observations of 363 

satellite of. 

deviations of its motion 360 

Venus, ancient theory of motion 39 

elements of orbit 

general description 

phases 296 

results of late transit 177 

transits of 177 

supposed axial rotation 297 

atmosphere 2 , .».' 

spectrum 301 

visibility of dark side 

satellite of, suspected B02 

Vogel, photogr. measures of Ban's rays. -'4. r . 

rotation of Venue 

spectrum of aurora 311 

views of Eucke'a comet 375 

Vortices, theory of. It 

Walker, motions of Neptune 37<> 

Week, days of the 40 

Wheatstone revolving mirror 290 

Winnecke, parallax of a star 211 

Wolf, periodicity of sun-spots 2M 

Wright, spectrum of zodiacal light 414 

Year, sidereal and tropical 20 

Young, constitution of the sun 2S2 

researches in spectrum analysis — 263 

Zodiac, definition of. 15 

signs of. 16 

Zodiacal light 295. 413 

Zollner, law of sun's rotation 250 

nature of photosphere 27'' 

intensity of moonlight 32." 

theory of comets 410 



EXPLANATION OF THE STAR MAPS. 

These maps show all the stars to the fifth magnitude inclusive be- 
tween the north pole and 40° south declination, the middle of each map 
extending to 50° declination. They therefore include all the stars which 
can be readily seen with the naked eye in our latitudes, except the very 
smallest. They are, for the most part, founded on Heis's Atlas CceJestis 
and the catalogue accompanying it. 

To recognize the constellations on the maps, reference may be had to 
the descriptions on pp. 418-426. To find what constellations are on the 
meridian at any hour of any day in the year, it will be necessary to cal- 
culate the sidereal time by the precepts on p. 151 : the corresponding hour 
of right ascension is then to be sought around the margin of Map I., and 
at the top and bottom of the other maps. Then, if Map I. be held with 
this hour upwards, it will show the exact position of the northern constel- 
lations, while on Maps II.- V. it will show the position of the meridian. 
Each of these four last maps extends about from the zenith to the south 
horizon. 

The several dates on the ecliptic show the positions of the sun during 
its apparent annual course as described in part i., chap, i., § 3, and ex- 
plained on pp. 54, 55. The apparent path of the moon in 1877 is marked 
out, in order to illustrate $ 6, p. 21. 

To illustrate precession, the position of the equator 2000 years ago is 
shown on Map II., where it can be compared with the present position, 
marked 0° on the sides of Maps II.— V. For the same object the circle 
which the celestial pole seems to describe around the pole of the ecliptic 
in 25,000 years is shown on Map I. 

The small circles marked here and there on the maps show the positions 
of the more remarkable nebulae and star clusters, a list of which is given 
in No. III. of the Appendix. 




Map I.— The Northern Constellations within 50° of the Pole. 




Map Il.-Southern Constellations visible in Autumn and Winter. 




Map IV-Southern Constellations visible in Spring and Sumnn 




Map "V.-Southern Constellations visible in Summer and Autumn. 




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